Warning: Permanently added '172.25.92.73' (ECDSA) to the list of known hosts.
Cloning into 'gap-pkg-automata'...
Note: checking out 'bbf9d279eb12318e3f6181d982bb66c54cbcacd3'.

You are in 'detached HEAD' state. You can look around, make experimental
changes and commit them, and you can discard any commits you make in this
state without impacting any branches by performing another checkout.

If you want to create a new branch to retain commits you create, you may
do so (now or later) by using -b with the checkout command again. Example:

  git checkout -b <new-branch-name>

HEAD is now at bbf9d27... import_srpm
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                                 Dload  Upload   Total   Spent    Left  Speed

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automata-1.13.tar.gz: OK
WARNING: Could not find required logging config file: /var/lib/copr-rpmbuild/results/configs/logging.ini. Using default...
INFO: mock.py version 1.4.2 starting (python version = 3.6.1)...
Start: init plugins
INFO: tmpfs initialized
INFO: selinux disabled
INFO: compress_logs: initialized
Finish: init plugins
Start: run
INFO: Start(gap-pkg-automata.spec)  Config(565363-epel-7-x86_64)
Start: clean chroot
Finish: clean chroot
Start: chroot init
INFO: mounting tmpfs at /var/lib/mock/565363-epel-7-x86_64/root.
INFO: calling preinit hooks
INFO: enabled root cache
INFO: enabled HW Info plugin
Mock Version: 1.4.2
INFO: Mock Version: 1.4.2
Start: yum install
Yum command has been deprecated, use dnf instead.
See 'man dnf' and 'man yum2dnf' for more information.


copr_base                                                   | 3.5 kB  00:00     

base                                                        | 3.6 kB  00:00     

epel                                                        | 4.3 kB  00:00     

extras                                                      | 3.4 kB  00:00     

updates                                                     | 3.4 kB  00:00     

(1/5): copr_base/primary_db                                 |  17 kB  00:00     

(3/5): epel/primary_db      0% [                 ]  0.0 B/s |  17 kB  --:-- ETA 

(2/5): extras/primary_db                                    | 167 kB  00:00     

(4/5): epel/primary_db     31% [=====            ] 7.3 MB/s | 5.1 MB  00:01 ETA 

(3/5): epel/primary_db                                      | 4.8 MB  00:00     

(5/5): updates/primary_db  59% [==========       ] 7.5 MB/s | 9.6 MB  00:00 ETA 

(4/5): base/primary_db     72% [============     ] 7.4 MB/s |  12 MB  00:00 ETA 

(4/5): updates/primary_db                                   | 5.7 MB  00:01     

(5/5): base/primary_db     84% [==============   ] 7.2 MB/s |  14 MB  00:00 ETA 

(5/5): base/primary_db     92% [===============- ] 6.9 MB/s |  15 MB  00:00 ETA 

(5/5): base/primary_db                                      | 5.6 MB  00:02     

base/group_gz                                               | 155 kB  00:00     

epel/group_gz                                               | 170 kB  00:00     
Resolving Dependencies
--> Running transaction check
---> Package bash.x86_64 0:4.2.46-21.el7_3 will be installed
--> Processing Dependency: rtld(GNU_HASH) for package: bash-4.2.46-21.el7_3.x86_64
--> Processing Dependency: libdl.so.2(GLIBC_2.2.5)(64bit) for package: bash-4.2.46-21.el7_3.x86_64
--> Processing Dependency: libc.so.6(GLIBC_2.8)(64bit) for package: bash-4.2.46-21.el7_3.x86_64
--> Processing Dependency: libtinfo.so.5()(64bit) for package: bash-4.2.46-21.el7_3.x86_64
--> Processing Dependency: libdl.so.2()(64bit) for package: bash-4.2.46-21.el7_3.x86_64
---> Package bzip2.x86_64 0:1.0.6-13.el7 will be installed
--> Processing Dependency: bzip2-libs = 1.0.6-13.el7 for package: bzip2-1.0.6-13.el7.x86_64
--> Processing Dependency: libbz2.so.1()(64bit) for package: bzip2-1.0.6-13.el7.x86_64
---> Package coreutils.x86_64 0:8.22-18.el7 will be installed
--> Processing Dependency: ncurses for package: coreutils-8.22-18.el7.x86_64
--> Processing Dependency: libcrypto.so.10(libcrypto.so.10)(64bit) for package: coreutils-8.22-18.el7.x86_64
--> Processing Dependency: libattr.so.1(ATTR_1.1)(64bit) for package: coreutils-8.22-18.el7.x86_64
--> Processing Dependency: libacl.so.1(ACL_1.0)(64bit) for package: coreutils-8.22-18.el7.x86_64
--> Processing Dependency: gmp for package: coreutils-8.22-18.el7.x86_64
--> Processing Dependency: libselinux.so.1()(64bit) for package: coreutils-8.22-18.el7.x86_64
--> Processing Dependency: libgmp.so.10()(64bit) for package: coreutils-8.22-18.el7.x86_64
--> Processing Dependency: libcrypto.so.10()(64bit) for package: coreutils-8.22-18.el7.x86_64
--> Processing Dependency: libcap.so.2()(64bit) for package: coreutils-8.22-18.el7.x86_64
--> Processing Dependency: libattr.so.1()(64bit) for package: coreutils-8.22-18.el7.x86_64
--> Processing Dependency: libacl.so.1()(64bit) for package: coreutils-8.22-18.el7.x86_64
---> Package cpio.x86_64 0:2.11-24.el7 will be installed
---> Package diffutils.x86_64 0:3.3-4.el7 will be installed
---> Package epel-release.noarch 0:7-9 will be installed
--> Processing Dependency: redhat-release >= 7 for package: epel-release-7-9.noarch
---> Package epel-rpm-macros.noarch 0:7-13 will be installed
--> Processing Dependency: python2-rpm-macros for package: epel-rpm-macros-7-13.noarch
--> Processing Dependency: python-srpm-macros for package: epel-rpm-macros-7-13.noarch
--> Processing Dependency: python-rpm-macros for package: epel-rpm-macros-7-13.noarch
---> Package findutils.x86_64 1:4.5.11-5.el7 will be installed
---> Package gawk.x86_64 0:4.0.2-4.el7 will be installed
---> Package gcc.x86_64 0:4.8.5-11.el7 will be installed
--> Processing Dependency: libgomp = 4.8.5-11.el7 for package: gcc-4.8.5-11.el7.x86_64
--> Processing Dependency: cpp = 4.8.5-11.el7 for package: gcc-4.8.5-11.el7.x86_64
--> Processing Dependency: libgcc >= 4.8.5-11.el7 for package: gcc-4.8.5-11.el7.x86_64
--> Processing Dependency: glibc-devel >= 2.2.90-12 for package: gcc-4.8.5-11.el7.x86_64
--> Processing Dependency: binutils >= 2.20.51.0.2-12 for package: gcc-4.8.5-11.el7.x86_64
--> Processing Dependency: libz.so.1()(64bit) for package: gcc-4.8.5-11.el7.x86_64
--> Processing Dependency: libmpfr.so.4()(64bit) for package: gcc-4.8.5-11.el7.x86_64
--> Processing Dependency: libmpc.so.3()(64bit) for package: gcc-4.8.5-11.el7.x86_64
--> Processing Dependency: libgomp.so.1()(64bit) for package: gcc-4.8.5-11.el7.x86_64
--> Processing Dependency: libgcc_s.so.1()(64bit) for package: gcc-4.8.5-11.el7.x86_64
---> Package gcc-c++.x86_64 0:4.8.5-11.el7 will be installed
--> Processing Dependency: libstdc++-devel = 4.8.5-11.el7 for package: gcc-c++-4.8.5-11.el7.x86_64
--> Processing Dependency: libstdc++ = 4.8.5-11.el7 for package: gcc-c++-4.8.5-11.el7.x86_64
--> Processing Dependency: libstdc++.so.6()(64bit) for package: gcc-c++-4.8.5-11.el7.x86_64
---> Package grep.x86_64 0:2.20-2.el7 will be installed
--> Processing Dependency: libpcre.so.1()(64bit) for package: grep-2.20-2.el7.x86_64
---> Package gzip.x86_64 0:1.5-8.el7 will be installed
---> Package info.x86_64 0:5.1-4.el7 will be installed
---> Package make.x86_64 1:3.82-23.el7 will be installed
---> Package patch.x86_64 0:2.7.1-8.el7 will be installed
---> Package redhat-rpm-config.noarch 0:9.1.0-72.el7.centos will be installed
--> Processing Dependency: rpm >= 4.9.0 for package: redhat-rpm-config-9.1.0-72.el7.centos.noarch
--> Processing Dependency: dwz >= 0.4 for package: redhat-rpm-config-9.1.0-72.el7.centos.noarch
--> Processing Dependency: zip for package: redhat-rpm-config-9.1.0-72.el7.centos.noarch
--> Processing Dependency: perl-srpm-macros for package: redhat-rpm-config-9.1.0-72.el7.centos.noarch
--> Processing Dependency: perl(Getopt::Long) for package: redhat-rpm-config-9.1.0-72.el7.centos.noarch
--> Processing Dependency: /usr/bin/perl for package: redhat-rpm-config-9.1.0-72.el7.centos.noarch
---> Package rpm-build.x86_64 0:4.11.3-21.el7 will be installed
--> Processing Dependency: pkgconfig >= 1:0.24 for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: elfutils >= 0.128 for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: perl(threads) for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: perl(Thread::Queue) for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: perl(File::Temp) for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: libpopt.so.0(LIBPOPT_0)(64bit) for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: libelf.so.1(ELFUTILS_1.0)(64bit) for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: file for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: /usr/bin/gdb-add-index for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: librpmio.so.3()(64bit) for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: librpmbuild.so.3()(64bit) for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: librpm.so.3()(64bit) for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: libpopt.so.0()(64bit) for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: libnss3.so()(64bit) for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: libmagic.so.1()(64bit) for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: liblzma.so.5()(64bit) for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: liblua-5.1.so()(64bit) for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: libelf.so.1()(64bit) for package: rpm-build-4.11.3-21.el7.x86_64
--> Processing Dependency: libdb-5.3.so()(64bit) for package: rpm-build-4.11.3-21.el7.x86_64
---> Package sed.x86_64 0:4.2.2-5.el7 will be installed
---> Package shadow-utils.x86_64 2:4.1.5.1-24.el7 will be installed
--> Processing Dependency: audit-libs >= 1.6.5 for package: 2:shadow-utils-4.1.5.1-24.el7.x86_64
--> Processing Dependency: setup for package: 2:shadow-utils-4.1.5.1-24.el7.x86_64
--> Processing Dependency: libsemanage.so.1(LIBSEMANAGE_1.0)(64bit) for package: 2:shadow-utils-4.1.5.1-24.el7.x86_64
--> Processing Dependency: libsemanage.so.1()(64bit) for package: 2:shadow-utils-4.1.5.1-24.el7.x86_64
--> Processing Dependency: libaudit.so.1()(64bit) for package: 2:shadow-utils-4.1.5.1-24.el7.x86_64
---> Package tar.x86_64 2:1.26-31.el7 will be installed
---> Package unzip.x86_64 0:6.0-16.el7 will be installed
---> Package util-linux.x86_64 0:2.23.2-33.el7_3.2 will be installed
--> Processing Dependency: libuuid = 2.23.2-33.el7_3.2 for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libmount = 2.23.2-33.el7_3.2 for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libblkid = 2.23.2-33.el7_3.2 for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: pam >= 1.1.3-7 for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libuuid.so.1(UUID_1.0)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libutempter.so.0(UTEMPTER_1.1)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libudev.so.1(LIBUDEV_183)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libsystemd.so.0(LIBSYSTEMD_209)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libpam_misc.so.0(LIBPAM_MISC_1.0)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libpam.so.0(LIBPAM_1.0)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libmount.so.1(MOUNT_2.25)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libmount.so.1(MOUNT_2.23)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libmount.so.1(MOUNT_2.22)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libmount.so.1(MOUNT_2.21)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libmount.so.1(MOUNT_2.20)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libmount.so.1(MOUNT_2.19)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libblkid.so.1(BLKID_2.21)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libblkid.so.1(BLKID_2.20)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libblkid.so.1(BLKID_2.18)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libblkid.so.1(BLKID_2.17)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libblkid.so.1(BLKID_2.15)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libblkid.so.1(BLKID_1.0)(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: /etc/pam.d/system-auth for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libuuid.so.1()(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libutempter.so.0()(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libuser.so.1()(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libudev.so.1()(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libsystemd.so.0()(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libpam_misc.so.0()(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libpam.so.0()(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libmount.so.1()(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libcap-ng.so.0()(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
--> Processing Dependency: libblkid.so.1()(64bit) for package: util-linux-2.23.2-33.el7_3.2.x86_64
---> Package which.x86_64 0:2.20-7.el7 will be installed
---> Package xz.x86_64 0:5.2.2-1.el7 will be installed
--> Running transaction check
---> Package audit-libs.x86_64 0:2.6.5-3.el7_3.1 will be installed
---> Package binutils.x86_64 0:2.25.1-22.base.el7 will be installed
--> Processing Dependency: /usr/sbin/alternatives for package: binutils-2.25.1-22.base.el7.x86_64
--> Processing Dependency: /usr/sbin/alternatives for package: binutils-2.25.1-22.base.el7.x86_64
---> Package bzip2-libs.x86_64 0:1.0.6-13.el7 will be installed
---> Package centos-release.x86_64 0:7-3.1611.el7.centos will be installed
---> Package cpp.x86_64 0:4.8.5-11.el7 will be installed
--> Processing Dependency: filesystem >= 3 for package: cpp-4.8.5-11.el7.x86_64
---> Package dwz.x86_64 0:0.11-3.el7 will be installed
---> Package elfutils.x86_64 0:0.166-2.el7 will be installed
--> Processing Dependency: elfutils-libs(x86-64) = 0.166-2.el7 for package: elfutils-0.166-2.el7.x86_64
--> Processing Dependency: libdw.so.1(ELFUTILS_0.165)(64bit) for package: elfutils-0.166-2.el7.x86_64
--> Processing Dependency: libdw.so.1(ELFUTILS_0.158)(64bit) for package: elfutils-0.166-2.el7.x86_64
--> Processing Dependency: libdw.so.1(ELFUTILS_0.149)(64bit) for package: elfutils-0.166-2.el7.x86_64
--> Processing Dependency: libdw.so.1(ELFUTILS_0.148)(64bit) for package: elfutils-0.166-2.el7.x86_64
--> Processing Dependency: libdw.so.1(ELFUTILS_0.138)(64bit) for package: elfutils-0.166-2.el7.x86_64
--> Processing Dependency: libdw.so.1(ELFUTILS_0.130)(64bit) for package: elfutils-0.166-2.el7.x86_64
--> Processing Dependency: libdw.so.1(ELFUTILS_0.127)(64bit) for package: elfutils-0.166-2.el7.x86_64
--> Processing Dependency: libdw.so.1(ELFUTILS_0.126)(64bit) for package: elfutils-0.166-2.el7.x86_64
--> Processing Dependency: libdw.so.1(ELFUTILS_0.122)(64bit) for package: elfutils-0.166-2.el7.x86_64
--> Processing Dependency: libasm.so.1(ELFUTILS_1.0)(64bit) for package: elfutils-0.166-2.el7.x86_64
--> Processing Dependency: libdw.so.1()(64bit) for package: elfutils-0.166-2.el7.x86_64
--> Processing Dependency: libasm.so.1()(64bit) for package: elfutils-0.166-2.el7.x86_64
---> Package elfutils-libelf.x86_64 0:0.166-2.el7 will be installed
---> Package file.x86_64 0:5.11-33.el7 will be installed
---> Package file-libs.x86_64 0:5.11-33.el7 will be installed
---> Package gdb.x86_64 0:7.6.1-94.el7 will be installed
--> Processing Dependency: libreadline.so.6()(64bit) for package: gdb-7.6.1-94.el7.x86_64
--> Processing Dependency: libpython2.7.so.1.0()(64bit) for package: gdb-7.6.1-94.el7.x86_64
--> Processing Dependency: libexpat.so.1()(64bit) for package: gdb-7.6.1-94.el7.x86_64
---> Package glibc.x86_64 0:2.17-157.el7_3.2 will be installed
--> Processing Dependency: glibc-common = 2.17-157.el7_3.2 for package: glibc-2.17-157.el7_3.2.x86_64
--> Processing Dependency: libfreebl3.so(NSSRAWHASH_3.12.3)(64bit) for package: glibc-2.17-157.el7_3.2.x86_64
--> Processing Dependency: basesystem for package: glibc-2.17-157.el7_3.2.x86_64
--> Processing Dependency: libfreebl3.so()(64bit) for package: glibc-2.17-157.el7_3.2.x86_64
---> Package glibc-devel.x86_64 0:2.17-157.el7_3.2 will be installed
--> Processing Dependency: glibc-headers = 2.17-157.el7_3.2 for package: glibc-devel-2.17-157.el7_3.2.x86_64
--> Processing Dependency: glibc-headers for package: glibc-devel-2.17-157.el7_3.2.x86_64
---> Package gmp.x86_64 1:6.0.0-12.el7_1 will be installed
---> Package libacl.x86_64 0:2.2.51-12.el7 will be installed
---> Package libattr.x86_64 0:2.4.46-12.el7 will be installed
---> Package libblkid.x86_64 0:2.23.2-33.el7_3.2 will be installed
---> Package libcap.x86_64 0:2.22-8.el7 will be installed
---> Package libcap-ng.x86_64 0:0.7.5-4.el7 will be installed
---> Package libdb.x86_64 0:5.3.21-19.el7 will be installed
---> Package libgcc.x86_64 0:4.8.5-11.el7 will be installed
---> Package libgomp.x86_64 0:4.8.5-11.el7 will be installed
---> Package libmount.x86_64 0:2.23.2-33.el7_3.2 will be installed
---> Package libmpc.x86_64 0:1.0.1-3.el7 will be installed
---> Package libselinux.x86_64 0:2.5-6.el7 will be installed
--> Processing Dependency: libsepol(x86-64) >= 2.5-6 for package: libselinux-2.5-6.el7.x86_64
--> Processing Dependency: libsepol.so.1(LIBSEPOL_1.0)(64bit) for package: libselinux-2.5-6.el7.x86_64
--> Processing Dependency: libsepol.so.1()(64bit) for package: libselinux-2.5-6.el7.x86_64
---> Package libsemanage.x86_64 0:2.5-5.1.el7_3 will be installed
--> Processing Dependency: libustr-1.0.so.1(USTR_1.0.1)(64bit) for package: libsemanage-2.5-5.1.el7_3.x86_64
--> Processing Dependency: libustr-1.0.so.1(USTR_1.0)(64bit) for package: libsemanage-2.5-5.1.el7_3.x86_64
--> Processing Dependency: libustr-1.0.so.1()(64bit) for package: libsemanage-2.5-5.1.el7_3.x86_64
---> Package libstdc++.x86_64 0:4.8.5-11.el7 will be installed
---> Package libstdc++-devel.x86_64 0:4.8.5-11.el7 will be installed
---> Package libuser.x86_64 0:0.60-7.el7_1 will be installed
--> Processing Dependency: libldap-2.4.so.2()(64bit) for package: libuser-0.60-7.el7_1.x86_64
--> Processing Dependency: libgobject-2.0.so.0()(64bit) for package: libuser-0.60-7.el7_1.x86_64
--> Processing Dependency: libgmodule-2.0.so.0()(64bit) for package: libuser-0.60-7.el7_1.x86_64
--> Processing Dependency: libglib-2.0.so.0()(64bit) for package: libuser-0.60-7.el7_1.x86_64
---> Package libutempter.x86_64 0:1.1.6-4.el7 will be installed
---> Package libuuid.x86_64 0:2.23.2-33.el7_3.2 will be installed
---> Package lua.x86_64 0:5.1.4-15.el7 will be installed
---> Package mpfr.x86_64 0:3.1.1-4.el7 will be installed
---> Package ncurses.x86_64 0:5.9-13.20130511.el7 will be installed
---> Package ncurses-libs.x86_64 0:5.9-13.20130511.el7 will be installed
--> Processing Dependency: ncurses-base = 5.9-13.20130511.el7 for package: ncurses-libs-5.9-13.20130511.el7.x86_64
---> Package nss.x86_64 0:3.28.4-1.2.el7_3 will be installed
--> Processing Dependency: nss-util >= 3.28.2-1.1 for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: nss-softokn(x86-64) >= 3.16.2.3-14.2 for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: nspr >= 4.13.1 for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: nss-system-init for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libnssutil3.so(NSSUTIL_3.24)(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libnssutil3.so(NSSUTIL_3.21)(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libnssutil3.so(NSSUTIL_3.17.1)(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libnssutil3.so(NSSUTIL_3.15)(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libnssutil3.so(NSSUTIL_3.14)(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libnssutil3.so(NSSUTIL_3.13)(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libnssutil3.so(NSSUTIL_3.12.5)(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libnssutil3.so(NSSUTIL_3.12.3)(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libnssutil3.so(NSSUTIL_3.12)(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libsoftokn3.so()(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libplds4.so()(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libplc4.so()(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libnssutil3.so()(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libnssdbm3.so()(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
--> Processing Dependency: libnspr4.so()(64bit) for package: nss-3.28.4-1.2.el7_3.x86_64
---> Package openssl-libs.x86_64 1:1.0.1e-60.el7_3.1 will be installed
--> Processing Dependency: ca-certificates >= 2008-5 for package: 1:openssl-libs-1.0.1e-60.el7_3.1.x86_64
--> Processing Dependency: libkrb5.so.3(krb5_3_MIT)(64bit) for package: 1:openssl-libs-1.0.1e-60.el7_3.1.x86_64
--> Processing Dependency: libk5crypto.so.3(k5crypto_3_MIT)(64bit) for package: 1:openssl-libs-1.0.1e-60.el7_3.1.x86_64
--> Processing Dependency: libkrb5.so.3()(64bit) for package: 1:openssl-libs-1.0.1e-60.el7_3.1.x86_64
--> Processing Dependency: libk5crypto.so.3()(64bit) for package: 1:openssl-libs-1.0.1e-60.el7_3.1.x86_64
--> Processing Dependency: libgssapi_krb5.so.2()(64bit) for package: 1:openssl-libs-1.0.1e-60.el7_3.1.x86_64
--> Processing Dependency: libcom_err.so.2()(64bit) for package: 1:openssl-libs-1.0.1e-60.el7_3.1.x86_64
---> Package pam.x86_64 0:1.1.8-18.el7 will be installed
--> Processing Dependency: libpwquality >= 0.9.9 for package: pam-1.1.8-18.el7.x86_64
--> Processing Dependency: cracklib-dicts >= 2.8 for package: pam-1.1.8-18.el7.x86_64
--> Processing Dependency: libcrack.so.2()(64bit) for package: pam-1.1.8-18.el7.x86_64
---> Package pcre.x86_64 0:8.32-15.el7_2.1 will be installed
---> Package perl.x86_64 4:5.16.3-291.el7 will be installed
--> Processing Dependency: perl-libs = 4:5.16.3-291.el7 for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(Socket) >= 1.3 for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(Scalar::Util) >= 1.10 for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl-macros for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl-libs for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(threads::shared) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(constant) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(Time::Local) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(Time::HiRes) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(Storable) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(Socket) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(Scalar::Util) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(Pod::Simple::XHTML) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(Pod::Simple::Search) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(Filter::Util::Call) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(File::Spec::Unix) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(File::Spec::Functions) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(File::Spec) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(File::Path) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(Exporter) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(Cwd) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: perl(Carp) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: libperl.so()(64bit) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: libgdbm_compat.so.4()(64bit) for package: 4:perl-5.16.3-291.el7.x86_64
--> Processing Dependency: libgdbm.so.4()(64bit) for package: 4:perl-5.16.3-291.el7.x86_64
---> Package perl-File-Temp.noarch 0:0.23.01-3.el7 will be installed
---> Package perl-Getopt-Long.noarch 0:2.40-2.el7 will be installed
--> Processing Dependency: perl(Pod::Usage) >= 1.14 for package: perl-Getopt-Long-2.40-2.el7.noarch
--> Processing Dependency: perl(Text::ParseWords) for package: perl-Getopt-Long-2.40-2.el7.noarch
---> Package perl-Thread-Queue.noarch 0:3.02-2.el7 will be installed
---> Package perl-srpm-macros.noarch 0:1-8.el7 will be installed
---> Package perl-threads.x86_64 0:1.87-4.el7 will be installed
---> Package pkgconfig.x86_64 1:0.27.1-4.el7 will be installed
---> Package popt.x86_64 0:1.13-16.el7 will be installed
---> Package python-rpm-macros.noarch 0:3-17.el7 will be installed
---> Package python-srpm-macros.noarch 0:3-17.el7 will be installed
---> Package python2-rpm-macros.noarch 0:3-17.el7 will be installed
---> Package rpm.x86_64 0:4.11.3-21.el7 will be installed
--> Processing Dependency: curl for package: rpm-4.11.3-21.el7.x86_64
--> Processing Dependency: /usr/bin/db_stat for package: rpm-4.11.3-21.el7.x86_64
---> Package rpm-build-libs.x86_64 0:4.11.3-21.el7 will be installed
--> Processing Dependency: /usr/bin/gpg2 for package: rpm-build-libs-4.11.3-21.el7.x86_64
---> Package rpm-libs.x86_64 0:4.11.3-21.el7 will be installed
---> Package setup.noarch 0:2.8.71-7.el7 will be installed
---> Package systemd-libs.x86_64 0:219-30.el7_3.9 will be installed
--> Processing Dependency: libgcrypt.so.11(GCRYPT_1.2)(64bit) for package: systemd-libs-219-30.el7_3.9.x86_64
--> Processing Dependency: libgpg-error.so.0()(64bit) for package: systemd-libs-219-30.el7_3.9.x86_64
--> Processing Dependency: libgcrypt.so.11()(64bit) for package: systemd-libs-219-30.el7_3.9.x86_64
---> Package xz-libs.x86_64 0:5.2.2-1.el7 will be installed
---> Package zip.x86_64 0:3.0-11.el7 will be installed
---> Package zlib.x86_64 0:1.2.7-17.el7 will be installed
--> Running transaction check
---> Package basesystem.noarch 0:10.0-7.el7.centos will be installed
---> Package ca-certificates.noarch 0:2017.2.14-70.1.el7_3 will be installed
--> Processing Dependency: p11-kit-trust >= 0.17.3 for package: ca-certificates-2017.2.14-70.1.el7_3.noarch
--> Processing Dependency: p11-kit >= 0.17.3 for package: ca-certificates-2017.2.14-70.1.el7_3.noarch
---> Package chkconfig.x86_64 0:1.7.2-1.el7 will be installed
---> Package cracklib.x86_64 0:2.9.0-11.el7 will be installed
---> Package cracklib-dicts.x86_64 0:2.9.0-11.el7 will be installed
---> Package curl.x86_64 0:7.29.0-35.el7.centos will be installed
--> Processing Dependency: libcurl = 7.29.0-35.el7.centos for package: curl-7.29.0-35.el7.centos.x86_64
--> Processing Dependency: libcurl.so.4()(64bit) for package: curl-7.29.0-35.el7.centos.x86_64
---> Package elfutils-libs.x86_64 0:0.166-2.el7 will be installed
---> Package expat.x86_64 0:2.1.0-10.el7_3 will be installed
---> Package filesystem.x86_64 0:3.2-21.el7 will be installed
---> Package gdbm.x86_64 0:1.10-8.el7 will be installed
---> Package glib2.x86_64 0:2.46.2-4.el7 will be installed
--> Processing Dependency: shared-mime-info for package: glib2-2.46.2-4.el7.x86_64
--> Processing Dependency: libffi.so.6()(64bit) for package: glib2-2.46.2-4.el7.x86_64
---> Package glibc-common.x86_64 0:2.17-157.el7_3.2 will be installed
--> Processing Dependency: tzdata >= 2003a for package: glibc-common-2.17-157.el7_3.2.x86_64
---> Package glibc-headers.x86_64 0:2.17-157.el7_3.2 will be installed
--> Processing Dependency: kernel-headers >= 2.2.1 for package: glibc-headers-2.17-157.el7_3.2.x86_64
--> Processing Dependency: kernel-headers for package: glibc-headers-2.17-157.el7_3.2.x86_64
---> Package gnupg2.x86_64 0:2.0.22-4.el7 will be installed
--> Processing Dependency: pinentry for package: gnupg2-2.0.22-4.el7.x86_64
--> Processing Dependency: libassuan.so.0(LIBASSUAN_1.0)(64bit) for package: gnupg2-2.0.22-4.el7.x86_64
--> Processing Dependency: libpth.so.20()(64bit) for package: gnupg2-2.0.22-4.el7.x86_64
--> Processing Dependency: libassuan.so.0()(64bit) for package: gnupg2-2.0.22-4.el7.x86_64
---> Package krb5-libs.x86_64 0:1.14.1-27.el7_3 will be installed
--> Processing Dependency: keyutils-libs >= 1.5.8 for package: krb5-libs-1.14.1-27.el7_3.x86_64
--> Processing Dependency: libkeyutils.so.1(KEYUTILS_1.5)(64bit) for package: krb5-libs-1.14.1-27.el7_3.x86_64
--> Processing Dependency: libkeyutils.so.1(KEYUTILS_1.0)(64bit) for package: krb5-libs-1.14.1-27.el7_3.x86_64
--> Processing Dependency: libkeyutils.so.1(KEYUTILS_0.3)(64bit) for package: krb5-libs-1.14.1-27.el7_3.x86_64
--> Processing Dependency: libverto.so.1()(64bit) for package: krb5-libs-1.14.1-27.el7_3.x86_64
--> Processing Dependency: libkeyutils.so.1()(64bit) for package: krb5-libs-1.14.1-27.el7_3.x86_64
---> Package libcom_err.x86_64 0:1.42.9-9.el7 will be installed
---> Package libdb-utils.x86_64 0:5.3.21-19.el7 will be installed
---> Package libgcrypt.x86_64 0:1.5.3-13.el7_3.1 will be installed
---> Package libgpg-error.x86_64 0:1.12-3.el7 will be installed
---> Package libpwquality.x86_64 0:1.2.3-4.el7 will be installed
---> Package libsepol.x86_64 0:2.5-6.el7 will be installed
---> Package ncurses-base.noarch 0:5.9-13.20130511.el7 will be installed
---> Package nspr.x86_64 0:4.13.1-1.0.el7_3 will be installed
---> Package nss-softokn.x86_64 0:3.16.2.3-14.4.el7 will be installed
--> Processing Dependency: libsqlite3.so.0()(64bit) for package: nss-softokn-3.16.2.3-14.4.el7.x86_64
---> Package nss-softokn-freebl.x86_64 0:3.16.2.3-14.4.el7 will be installed
---> Package nss-sysinit.x86_64 0:3.28.4-1.2.el7_3 will be installed
---> Package nss-util.x86_64 0:3.28.4-1.0.el7_3 will be installed
---> Package openldap.x86_64 0:2.4.40-13.el7 will be installed
--> Processing Dependency: nss-tools for package: openldap-2.4.40-13.el7.x86_64
--> Processing Dependency: libsasl2.so.3()(64bit) for package: openldap-2.4.40-13.el7.x86_64
---> Package perl-Carp.noarch 0:1.26-244.el7 will be installed
---> Package perl-Exporter.noarch 0:5.68-3.el7 will be installed
---> Package perl-File-Path.noarch 0:2.09-2.el7 will be installed
---> Package perl-Filter.x86_64 0:1.49-3.el7 will be installed
---> Package perl-PathTools.x86_64 0:3.40-5.el7 will be installed
---> Package perl-Pod-Simple.noarch 1:3.28-4.el7 will be installed
--> Processing Dependency: perl(Pod::Escapes) >= 1.04 for package: 1:perl-Pod-Simple-3.28-4.el7.noarch
--> Processing Dependency: perl(Encode) for package: 1:perl-Pod-Simple-3.28-4.el7.noarch
---> Package perl-Pod-Usage.noarch 0:1.63-3.el7 will be installed
--> Processing Dependency: perl(Pod::Text) >= 3.15 for package: perl-Pod-Usage-1.63-3.el7.noarch
--> Processing Dependency: perl-Pod-Perldoc for package: perl-Pod-Usage-1.63-3.el7.noarch
---> Package perl-Scalar-List-Utils.x86_64 0:1.27-248.el7 will be installed
---> Package perl-Socket.x86_64 0:2.010-4.el7 will be installed
---> Package perl-Storable.x86_64 0:2.45-3.el7 will be installed
---> Package perl-Text-ParseWords.noarch 0:3.29-4.el7 will be installed
---> Package perl-Time-HiRes.x86_64 4:1.9725-3.el7 will be installed
---> Package perl-Time-Local.noarch 0:1.2300-2.el7 will be installed
---> Package perl-constant.noarch 0:1.27-2.el7 will be installed
---> Package perl-libs.x86_64 4:5.16.3-291.el7 will be installed
---> Package perl-macros.x86_64 4:5.16.3-291.el7 will be installed
---> Package perl-threads-shared.x86_64 0:1.43-6.el7 will be installed
---> Package python-libs.x86_64 0:2.7.5-48.el7 will be installed
---> Package readline.x86_64 0:6.2-9.el7 will be installed
---> Package ustr.x86_64 0:1.0.4-16.el7 will be installed
--> Running transaction check
---> Package cyrus-sasl-lib.x86_64 0:2.1.26-20.el7_2 will be installed
---> Package kernel-headers.x86_64 0:3.10.0-514.21.1.el7 will be installed
---> Package keyutils-libs.x86_64 0:1.5.8-3.el7 will be installed
---> Package libassuan.x86_64 0:2.1.0-3.el7 will be installed
---> Package libcurl.x86_64 0:7.29.0-35.el7.centos will be installed
--> Processing Dependency: libssh2(x86-64) >= 1.4.3 for package: libcurl-7.29.0-35.el7.centos.x86_64
--> Processing Dependency: libidn.so.11(LIBIDN_1.0)(64bit) for package: libcurl-7.29.0-35.el7.centos.x86_64
--> Processing Dependency: libssh2.so.1()(64bit) for package: libcurl-7.29.0-35.el7.centos.x86_64
--> Processing Dependency: libidn.so.11()(64bit) for package: libcurl-7.29.0-35.el7.centos.x86_64
---> Package libffi.x86_64 0:3.0.13-18.el7 will be installed
---> Package libverto.x86_64 0:0.2.5-4.el7 will be installed
---> Package nss-tools.x86_64 0:3.28.4-1.2.el7_3 will be installed
---> Package p11-kit.x86_64 0:0.20.7-3.el7 will be installed
---> Package p11-kit-trust.x86_64 0:0.20.7-3.el7 will be installed
--> Processing Dependency: libtasn1.so.6(LIBTASN1_0_3)(64bit) for package: p11-kit-trust-0.20.7-3.el7.x86_64
--> Processing Dependency: libtasn1.so.6()(64bit) for package: p11-kit-trust-0.20.7-3.el7.x86_64
---> Package perl-Encode.x86_64 0:2.51-7.el7 will be installed
---> Package perl-Pod-Escapes.noarch 1:1.04-291.el7 will be installed
---> Package perl-Pod-Perldoc.noarch 0:3.20-4.el7 will be installed
--> Processing Dependency: perl(parent) for package: perl-Pod-Perldoc-3.20-4.el7.noarch
--> Processing Dependency: perl(HTTP::Tiny) for package: perl-Pod-Perldoc-3.20-4.el7.noarch
--> Processing Dependency: groff-base for package: perl-Pod-Perldoc-3.20-4.el7.noarch
---> Package perl-podlators.noarch 0:2.5.1-3.el7 will be installed
---> Package pinentry.x86_64 0:0.8.1-17.el7 will be installed
---> Package pth.x86_64 0:2.0.7-23.el7 will be installed
---> Package shared-mime-info.x86_64 0:1.1-9.el7 will be installed
--> Processing Dependency: libxml2.so.2(LIBXML2_2.4.30)(64bit) for package: shared-mime-info-1.1-9.el7.x86_64
--> Processing Dependency: libxml2.so.2()(64bit) for package: shared-mime-info-1.1-9.el7.x86_64
---> Package sqlite.x86_64 0:3.7.17-8.el7 will be installed
---> Package tzdata.noarch 0:2017b-1.el7 will be installed
--> Running transaction check
---> Package groff-base.x86_64 0:1.22.2-8.el7 will be installed
---> Package libidn.x86_64 0:1.28-4.el7 will be installed
---> Package libssh2.x86_64 0:1.4.3-10.el7_2.1 will be installed
---> Package libtasn1.x86_64 0:3.8-3.el7 will be installed
---> Package libxml2.x86_64 0:2.9.1-6.el7_2.3 will be installed
---> Package perl-HTTP-Tiny.noarch 0:0.033-3.el7 will be installed
---> Package perl-parent.noarch 1:0.225-244.el7 will be installed
--> Finished Dependency Resolution

Dependencies Resolved

================================================================================
 Package                   Arch      Version                   Repository  Size
================================================================================
Installing for group install "Buildsystem building group":
 bash                      x86_64    4.2.46-21.el7_3           updates    1.0 M
 bzip2                     x86_64    1.0.6-13.el7              base        52 k
 coreutils                 x86_64    8.22-18.el7               base       3.3 M
 cpio                      x86_64    2.11-24.el7               base       210 k
 diffutils                 x86_64    3.3-4.el7                 base       322 k
 epel-release              noarch    7-9                       epel        14 k
 epel-rpm-macros           noarch    7-13                      epel        12 k
 findutils                 x86_64    1:4.5.11-5.el7            base       559 k
 gawk                      x86_64    4.0.2-4.el7               base       873 k
 gcc                       x86_64    4.8.5-11.el7              base        16 M
 gcc-c++                   x86_64    4.8.5-11.el7              base       7.2 M
 grep                      x86_64    2.20-2.el7                base       344 k
 gzip                      x86_64    1.5-8.el7                 base       129 k
 info                      x86_64    5.1-4.el7                 base       233 k
 make                      x86_64    1:3.82-23.el7             base       420 k
 patch                     x86_64    2.7.1-8.el7               base       110 k
 redhat-rpm-config         noarch    9.1.0-72.el7.centos       base        78 k
 rpm-build                 x86_64    4.11.3-21.el7             base       145 k
 sed                       x86_64    4.2.2-5.el7               base       231 k
 shadow-utils              x86_64    2:4.1.5.1-24.el7          base       1.1 M
 tar                       x86_64    2:1.26-31.el7             base       843 k
 unzip                     x86_64    6.0-16.el7                base       169 k
 util-linux                x86_64    2.23.2-33.el7_3.2         updates    1.9 M
 which                     x86_64    2.20-7.el7                base        41 k
 xz                        x86_64    5.2.2-1.el7               base       229 k
Installing for dependencies:
 audit-libs                x86_64    2.6.5-3.el7_3.1           updates     85 k
 basesystem                noarch    10.0-7.el7.centos         base       5.0 k
 binutils                  x86_64    2.25.1-22.base.el7        base       5.4 M
 bzip2-libs                x86_64    1.0.6-13.el7              base        40 k
 ca-certificates           noarch    2017.2.14-70.1.el7_3      updates    438 k
 centos-release            x86_64    7-3.1611.el7.centos       base        23 k
 chkconfig                 x86_64    1.7.2-1.el7               base       175 k
 cpp                       x86_64    4.8.5-11.el7              base       5.9 M
 cracklib                  x86_64    2.9.0-11.el7              base        80 k
 cracklib-dicts            x86_64    2.9.0-11.el7              base       3.6 M
 curl                      x86_64    7.29.0-35.el7.centos      base       265 k
 cyrus-sasl-lib            x86_64    2.1.26-20.el7_2           base       155 k
 dwz                       x86_64    0.11-3.el7                base        99 k
 elfutils                  x86_64    0.166-2.el7               base       280 k
 elfutils-libelf           x86_64    0.166-2.el7               base       208 k
 elfutils-libs             x86_64    0.166-2.el7               base       262 k
 expat                     x86_64    2.1.0-10.el7_3            updates     81 k
 file                      x86_64    5.11-33.el7               base        57 k
 file-libs                 x86_64    5.11-33.el7               base       340 k
 filesystem                x86_64    3.2-21.el7                base       1.0 M
 gdb                       x86_64    7.6.1-94.el7              base       2.4 M
 gdbm                      x86_64    1.10-8.el7                base        70 k
 glib2                     x86_64    2.46.2-4.el7              base       2.3 M
 glibc                     x86_64    2.17-157.el7_3.2          updates    3.6 M
 glibc-common              x86_64    2.17-157.el7_3.2          updates     11 M
 glibc-devel               x86_64    2.17-157.el7_3.2          updates    1.1 M
 glibc-headers             x86_64    2.17-157.el7_3.2          updates    669 k
 gmp                       x86_64    1:6.0.0-12.el7_1          base       280 k
 gnupg2                    x86_64    2.0.22-4.el7              base       1.5 M
 groff-base                x86_64    1.22.2-8.el7              base       942 k
 kernel-headers            x86_64    3.10.0-514.21.1.el7       updates    4.8 M
 keyutils-libs             x86_64    1.5.8-3.el7               base        25 k
 krb5-libs                 x86_64    1.14.1-27.el7_3           updates    740 k
 libacl                    x86_64    2.2.51-12.el7             base        27 k
 libassuan                 x86_64    2.1.0-3.el7               base        63 k
 libattr                   x86_64    2.4.46-12.el7             base        18 k
 libblkid                  x86_64    2.23.2-33.el7_3.2         updates    170 k
 libcap                    x86_64    2.22-8.el7                base        47 k
 libcap-ng                 x86_64    0.7.5-4.el7               base        25 k
 libcom_err                x86_64    1.42.9-9.el7              base        40 k
 libcurl                   x86_64    7.29.0-35.el7.centos      base       218 k
 libdb                     x86_64    5.3.21-19.el7             base       718 k
 libdb-utils               x86_64    5.3.21-19.el7             base       102 k
 libffi                    x86_64    3.0.13-18.el7             base        30 k
 libgcc                    x86_64    4.8.5-11.el7              base        97 k
 libgcrypt                 x86_64    1.5.3-13.el7_3.1          updates    263 k
 libgomp                   x86_64    4.8.5-11.el7              base       152 k
 libgpg-error              x86_64    1.12-3.el7                base        87 k
 libidn                    x86_64    1.28-4.el7                base       209 k
 libmount                  x86_64    2.23.2-33.el7_3.2         updates    172 k
 libmpc                    x86_64    1.0.1-3.el7               base        51 k
 libpwquality              x86_64    1.2.3-4.el7               base        84 k
 libselinux                x86_64    2.5-6.el7                 base       161 k
 libsemanage               x86_64    2.5-5.1.el7_3             updates    144 k
 libsepol                  x86_64    2.5-6.el7                 base       288 k
 libssh2                   x86_64    1.4.3-10.el7_2.1          base       134 k
 libstdc++                 x86_64    4.8.5-11.el7              base       300 k
 libstdc++-devel           x86_64    4.8.5-11.el7              base       1.5 M
 libtasn1                  x86_64    3.8-3.el7                 base       320 k
 libuser                   x86_64    0.60-7.el7_1              base       398 k
 libutempter               x86_64    1.1.6-4.el7               base        25 k
 libuuid                   x86_64    2.23.2-33.el7_3.2         updates     76 k
 libverto                  x86_64    0.2.5-4.el7               base        16 k
 libxml2                   x86_64    2.9.1-6.el7_2.3           base       668 k
 lua                       x86_64    5.1.4-15.el7              base       201 k
 mpfr                      x86_64    3.1.1-4.el7               base       203 k
 ncurses                   x86_64    5.9-13.20130511.el7       base       303 k
 ncurses-base              noarch    5.9-13.20130511.el7       base        68 k
 ncurses-libs              x86_64    5.9-13.20130511.el7       base       316 k
 nspr                      x86_64    4.13.1-1.0.el7_3          updates    126 k
 nss                       x86_64    3.28.4-1.2.el7_3          updates    872 k
 nss-softokn               x86_64    3.16.2.3-14.4.el7         base       306 k
 nss-softokn-freebl        x86_64    3.16.2.3-14.4.el7         base       204 k
 nss-sysinit               x86_64    3.28.4-1.2.el7_3          updates     58 k
 nss-tools                 x86_64    3.28.4-1.2.el7_3          updates    496 k
 nss-util                  x86_64    3.28.4-1.0.el7_3          updates     73 k
 openldap                  x86_64    2.4.40-13.el7             base       350 k
 openssl-libs              x86_64    1:1.0.1e-60.el7_3.1       updates    959 k
 p11-kit                   x86_64    0.20.7-3.el7              base       107 k
 p11-kit-trust             x86_64    0.20.7-3.el7              base       126 k
 pam                       x86_64    1.1.8-18.el7              base       717 k
 pcre                      x86_64    8.32-15.el7_2.1           base       420 k
 perl                      x86_64    4:5.16.3-291.el7          base       8.0 M
 perl-Carp                 noarch    1.26-244.el7              base        19 k
 perl-Encode               x86_64    2.51-7.el7                base       1.5 M
 perl-Exporter             noarch    5.68-3.el7                base        28 k
 perl-File-Path            noarch    2.09-2.el7                base        26 k
 perl-File-Temp            noarch    0.23.01-3.el7             base        56 k
 perl-Filter               x86_64    1.49-3.el7                base        76 k
 perl-Getopt-Long          noarch    2.40-2.el7                base        56 k
 perl-HTTP-Tiny            noarch    0.033-3.el7               base        38 k
 perl-PathTools            x86_64    3.40-5.el7                base        82 k
 perl-Pod-Escapes          noarch    1:1.04-291.el7            base        51 k
 perl-Pod-Perldoc          noarch    3.20-4.el7                base        87 k
 perl-Pod-Simple           noarch    1:3.28-4.el7              base       216 k
 perl-Pod-Usage            noarch    1.63-3.el7                base        27 k
 perl-Scalar-List-Utils    x86_64    1.27-248.el7              base        36 k
 perl-Socket               x86_64    2.010-4.el7               base        49 k
 perl-Storable             x86_64    2.45-3.el7                base        77 k
 perl-Text-ParseWords      noarch    3.29-4.el7                base        14 k
 perl-Thread-Queue         noarch    3.02-2.el7                base        17 k
 perl-Time-HiRes           x86_64    4:1.9725-3.el7            base        45 k
 perl-Time-Local           noarch    1.2300-2.el7              base        24 k
 perl-constant             noarch    1.27-2.el7                base        19 k
 perl-libs                 x86_64    4:5.16.3-291.el7          base       688 k
 perl-macros               x86_64    4:5.16.3-291.el7          base        43 k
 perl-parent               noarch    1:0.225-244.el7           base        12 k
 perl-podlators            noarch    2.5.1-3.el7               base       112 k
 perl-srpm-macros          noarch    1-8.el7                   base       4.6 k
 perl-threads              x86_64    1.87-4.el7                base        49 k
 perl-threads-shared       x86_64    1.43-6.el7                base        39 k
 pinentry                  x86_64    0.8.1-17.el7              base        73 k
 pkgconfig                 x86_64    1:0.27.1-4.el7            base        54 k
 popt                      x86_64    1.13-16.el7               base        42 k
 pth                       x86_64    2.0.7-23.el7              base        89 k
 python-libs               x86_64    2.7.5-48.el7              base       5.6 M
 python-rpm-macros         noarch    3-17.el7                  epel       6.1 k
 python-srpm-macros        noarch    3-17.el7                  epel       5.9 k
 python2-rpm-macros        noarch    3-17.el7                  epel       5.6 k
 readline                  x86_64    6.2-9.el7                 base       192 k
 rpm                       x86_64    4.11.3-21.el7             base       1.2 M
 rpm-build-libs            x86_64    4.11.3-21.el7             base       104 k
 rpm-libs                  x86_64    4.11.3-21.el7             base       274 k
 setup                     noarch    2.8.71-7.el7              base       165 k
 shared-mime-info          x86_64    1.1-9.el7                 base       371 k
 sqlite                    x86_64    3.7.17-8.el7              base       393 k
 systemd-libs              x86_64    219-30.el7_3.9            updates    369 k
 tzdata                    noarch    2017b-1.el7               updates    443 k
 ustr                      x86_64    1.0.4-16.el7              base        92 k
 xz-libs                   x86_64    5.2.2-1.el7               base       103 k
 zip                       x86_64    3.0-11.el7                base       260 k
 zlib                      x86_64    1.2.7-17.el7              base        90 k

Transaction Summary
================================================================================
Install  25 Packages (+132 Dependent packages)

Total download size: 117 M
Installed size: 427 M
Downloading packages:
warning: /var/lib/mock/565363-epel-7-x86_64/root/var/cache/yum/base/packages/basesystem-10.0-7.el7.centos.noarch.rpm: Header V3 RSA/SHA256 Signature, key ID f4a80eb5: NOKEY
Public key for basesystem-10.0-7.el7.centos.noarch.rpm is not installed

(1/157): basesystem-10.0-7.el7.centos.noarch.rpm            | 5.0 kB  00:00     
Public key for audit-libs-2.6.5-3.el7_3.1.x86_64.rpm is not installed

(2/157): audit-libs-2.6.5-3.el7_3.1.x86_64.rpm              |  85 kB  00:00     

(3/157): bzip2-1.0.6-13.el7.x86_64.rpm                      |  52 kB  00:00     

(4/157): bzip2-libs-1.0.6-13.el7.x86_64.rpm                 |  40 kB  00:00     

(5/157): centos-release-7-3.1611.el7.centos.x86_64.rpm      |  23 kB  00:00     

(7/157): binutils-2.25.1-22 0% [                 ]  0.0 B/s | 867 kB  --:-- ETA 

(6/157): ca-certificates-2017.2.14-70.1.el7_3.noarch.rpm    | 438 kB  00:00     

(7/157): bash-4.2.46-21.el7_3.x86_64.rpm                    | 1.0 MB  00:00     

(8/157): chkconfig-1.7.2-1.el7.x86_64.rpm                   | 175 kB  00:00     

(10/157): coreutils-8.22-18 2% [                 ] 1.8 MB/s | 2.5 MB  01:03 ETA 

(10/157): coreutils-8.22-18 3% [-                ] 1.9 MB/s | 3.6 MB  00:59 ETA 

(9/157): binutils-2.25.1-22 4% [-                ] 2.1 MB/s | 5.1 MB  00:54 ETA 

(9/157): binutils-2.25.1-22 5% [-                ] 2.3 MB/s | 6.9 MB  00:47 ETA 

(9/157): coreutils-8.22-18.el7.x86_64.rpm                   | 3.3 MB  00:01     

(10/157): binutils-2.25.1-2 8% [=                ] 2.7 MB/s | 9.4 MB  00:40 ETA 

(10/157): cpio-2.11-24.el7.x86_64.rpm                       | 210 kB  00:00     

(11/157): binutils-2.25.1-22.base.el7.x86_64.rpm            | 5.4 MB  00:02     

(12/157): cracklib-2.9.0-11.el7.x86_64.rpm                  |  80 kB  00:00     

(14/157): cracklib-dicts-2 10% [=-               ] 3.0 MB/s |  12 MB  00:34 ETA 

(14/157): cracklib-dicts-2 14% [==               ] 3.6 MB/s |  16 MB  00:27 ETA 

(13/157): cracklib-dicts-2.9.0-11.el7.x86_64.rpm            | 3.6 MB  00:00     

(14/157): curl-7.29.0-35.el7.centos.x86_64.rpm              | 265 kB  00:00     

(15/157): cyrus-sasl-lib-2.1.26-20.el7_2.x86_64.rpm         | 155 kB  00:00     

(16/157): cpp-4.8.5-11.el7.x86_64.rpm                       | 5.9 MB  00:01     

(17/157): diffutils-3.3-4.el7.x86_64.rpm                    | 322 kB  00:00     

(18/157): dwz-0.11-3.el7.x86_64.rpm                         |  99 kB  00:00     

(19/157): elfutils-0.166-2.el7.x86_64.rpm                   | 280 kB  00:00     

(20/157): elfutils-libelf-0.166-2.el7.x86_64.rpm            | 208 kB  00:00     

(21/157): elfutils-libs-0.166-2.el7.x86_64.rpm              | 262 kB  00:00     

(22/157): file-5.11-33.el7.x86_64.rpm                       |  57 kB  00:00     

(23/157): file-libs-5.11-33.el7.x86_64.rpm                  | 340 kB  00:00     

(24/157): expat-2.1.0-10.el7_3.x86_64.rpm                   |  81 kB  00:00     

(25/157): filesystem-3.2-21.el7.x86_64.rpm                  | 1.0 MB  00:00     

(26/157): findutils-4.5.11-5.el7.x86_64.rpm                 | 559 kB  00:00     

(27/157): gawk-4.0.2-4.el7.x86_64.rpm                       | 873 kB  00:00     

(30/157): gcc-4.8.5-11.el7 21% [===-             ] 4.7 MB/s |  25 MB  00:19 ETA 
warning: /var/lib/mock/565363-epel-7-x86_64/root/var/cache/yum/epel/packages/epel-rpm-macros-7-13.noarch.rpm: Header V3 RSA/SHA256 Signature, key ID 352c64e5: NOKEY
Public key for epel-rpm-macros-7-13.noarch.rpm is not installed

(28/157): epel-rpm-macros-7-13.noarch.rpm                   |  12 kB  00:00     

(29/157): epel-release-7-9.noarch.rpm                       |  14 kB  00:00     

(30/157): gcc-4.8.5-11.el7 26% [====-            ] 5.7 MB/s |  31 MB  00:15 ETA 

(30/157): gcc-4.8.5-11.el7 33% [=====-           ] 6.9 MB/s |  39 MB  00:11 ETA 

(30/157): gcc-c++-4.8.5-11.el7.x86_64.rpm                   | 7.2 MB  00:00     

(31/157): gcc-4.8.5-11.el7.x86_64.rpm                       |  16 MB  00:01     

(32/157): gdb-7.6.1-94.el7.x86_64.rpm                       | 2.4 MB  00:00     

(33/157): gdbm-1.10-8.el7.x86_64.rpm                        |  70 kB  00:00     

(34/157): glib2-2.46.2-4.el7.x86_64.rpm                     | 2.3 MB  00:00     

(36/157): glibc-common-2.1 45% [=======-         ] 8.7 MB/s |  53 MB  00:07 ETA 

(36/157): glibc-common-2.1 47% [========         ] 8.6 MB/s |  56 MB  00:07 ETA 

(35/157): glibc-2.17-157.el7_3.2.x86_64.rpm                 | 3.6 MB  00:00     

(36/157): glibc-devel-2.17-157.el7_3.2.x86_64.rpm           | 1.1 MB  00:00     

(37/157): glibc-headers-2.17-157.el7_3.2.x86_64.rpm         | 669 kB  00:00     

(39/157): gmp-6.0.0-12.el7 52% [=========        ] 9.0 MB/s |  62 MB  00:06 ETA 

(38/157): gmp-6.0.0-12.el7_1.x86_64.rpm                     | 280 kB  00:00     

(39/157): grep-2.20-2.el7.x86_64.rpm                        | 344 kB  00:00     

(42/157): groff-base-1.22. 54% [=========        ] 8.8 MB/s |  64 MB  00:06 ETA 

(40/157): groff-base-1.22.2-8.el7.x86_64.rpm                | 942 kB  00:00     

(41/157): gzip-1.5-8.el7.x86_64.rpm                         | 129 kB  00:00     

(42/157): info-5.1-4.el7.x86_64.rpm                         | 233 kB  00:00     

(43/157): keyutils-libs-1.5.8-3.el7.x86_64.rpm              |  25 kB  00:00     

(46/157): kernel-headers-3 56% [=========-       ] 8.7 MB/s |  66 MB  00:05 ETA 

(44/157): gnupg2-2.0.22-4.el7.x86_64.rpm                    | 1.5 MB  00:00     

(45/157): glibc-common-2.1 60% [==========       ] 9.1 MB/s |  71 MB  00:05 ETA 

(45/157): kernel-headers-3.10.0-514.21.1.el7.x86_64.rpm     | 4.8 MB  00:00     

(46/157): glibc-common-2.1 62% [==========-      ] 9.2 MB/s |  74 MB  00:04 ETA 

(46/157): libacl-2.2.51-12.el7.x86_64.rpm                   |  27 kB  00:00     

(47/157): libattr-2.4.46-12.el7.x86_64.rpm                  |  18 kB  00:00     

(48/157): krb5-libs-1.14.1-27.el7_3.x86_64.rpm              | 740 kB  00:00     

(49/157): libblkid-2.23.2-33.el7_3.2.x86_64.rpm             | 170 kB  00:00     

(50/157): libcap-2.22-8.el7.x86_64.rpm                      |  47 kB  00:00     

(51/157): libcap-ng-0.7.5-4.el7.x86_64.rpm                  |  25 kB  00:00     

(52/157): libassuan-2.1.0-3.el7.x86_64.rpm                  |  63 kB  00:00     

(53/157): libcom_err-1.42.9-9.el7.x86_64.rpm                |  40 kB  00:00     

(54/157): libdb-5.3.21-19.el7.x86_64.rpm                    | 718 kB  00:00     

(56/157): libcurl-7.29.0-3 64% [===========      ] 8.5 MB/s |  76 MB  00:04 ETA 

(55/157): libdb-utils-5.3.21-19.el7.x86_64.rpm              | 102 kB  00:00     

(56/157): libcurl-7.29.0-35.el7.centos.x86_64.rpm           | 218 kB  00:00     

(57/157): libffi-3.0.13-18.el7.x86_64.rpm                   |  30 kB  00:00     

(58/157): libgomp-4.8.5-11.el7.x86_64.rpm                   | 152 kB  00:00     

(59/157): libgcrypt-1.5.3-13.el7_3.1.x86_64.rpm             | 263 kB  00:00     

(60/157): libgpg-error-1.12-3.el7.x86_64.rpm                |  87 kB  00:00     

(61/157): libgcc-4.8.5-11.el7.x86_64.rpm                    |  97 kB  00:00     

(62/157): libmount-2.23.2-33.el7_3.2.x86_64.rpm             | 172 kB  00:00     

(63/157): libidn-1.28-4.el7.x86_64.rpm                      | 209 kB  00:00     

(65/157): libmpc-1.0.1-3.e 67% [===========      ] 8.5 MB/s |  79 MB  00:04 ETA 

(64/157): libpwquality-1.2.3-4.el7.x86_64.rpm               |  84 kB  00:00     

(65/157): libmpc-1.0.1-3.el7.x86_64.rpm                     |  51 kB  00:00     

(66/157): libsemanage-2.5-5.1.el7_3.x86_64.rpm              | 144 kB  00:00     

(67/157): libselinux-2.5-6.el7.x86_64.rpm                   | 161 kB  00:00     

(68/157): libssh2-1.4.3-10.el7_2.1.x86_64.rpm               | 134 kB  00:00     

(69/157): libstdc++-4.8.5-11.el7.x86_64.rpm                 | 300 kB  00:00     

(71/157): libsepol-2.5-6.e 68% [===========-     ] 8.3 MB/s |  80 MB  00:04 ETA 

(70/157): libstdc++-devel-4.8.5-11.el7.x86_64.rpm           | 1.5 MB  00:00     

(71/157): libtasn1-3.8-3.el7.x86_64.rpm                     | 320 kB  00:00     

(72/157): libsepol-2.5-6.el7.x86_64.rpm                     | 288 kB  00:00     

(73/157): libuuid-2.23.2-33.el7_3.2.x86_64.rpm              |  76 kB  00:00     

(74/157): libuser-0.60-7.el7_1.x86_64.rpm                   | 398 kB  00:00     

(75/157): libutempter-1.1.6-4.el7.x86_64.rpm                |  25 kB  00:00     

(76/157): libverto-0.2.5-4.el7.x86_64.rpm                   |  16 kB  00:00     

(78/157): libxml2-2.9.1-6. 71% [============     ] 8.6 MB/s |  84 MB  00:03 ETA 

(77/157): lua-5.1.4-15.el7.x86_64.rpm                       | 201 kB  00:00     

(78/157): glibc-common-2.17-157.el7_3.2.x86_64.rpm          |  11 MB  00:04     

(79/157): make-3.82-23.el7.x86_64.rpm                       | 420 kB  00:00     

(80/157): mpfr-3.1.1-4.el7.x86_64.rpm                       | 203 kB  00:00     

(81/157): ncurses-5.9-13.20130511.el7.x86_64.rpm            | 303 kB  00:00     

(82/157): ncurses-base-5.9-13.20130511.el7.noarch.rpm       |  68 kB  00:00     

(85/157): nspr-4.13.1-1.0. 73% [============     ] 8.4 MB/s |  86 MB  00:03 ETA 

(83/157): ncurses-libs-5.9-13.20130511.el7.x86_64.rpm       | 316 kB  00:00     

(84/157): nspr-4.13.1-1.0.el7_3.x86_64.rpm                  | 126 kB  00:00     

(85/157): nss-softokn-3.16.2.3-14.4.el7.x86_64.rpm          | 306 kB  00:00     

(86/157): nss-sysinit-3.28.4-1.2.el7_3.x86_64.rpm           |  58 kB  00:00     

(87/157): nss-softokn-freebl-3.16.2.3-14.4.el7.x86_64.rpm   | 204 kB  00:00     

(88/157): nss-tools-3.28.4-1.2.el7_3.x86_64.rpm             | 496 kB  00:00     

(91/157): nss-util-3.28.4- 74% [============-    ] 8.1 MB/s |  88 MB  00:03 ETA 

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(91/157): openldap-2.4.40-13.el7.x86_64.rpm                 | 350 kB  00:00     

(92/157): p11-kit-trust-0.20.7-3.el7.x86_64.rpm             | 126 kB  00:00     

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(95/157): pam-1.1.8-18.el7.x86_64.rpm                       | 717 kB  00:00     

(96/157): pcre-8.32-15.el7_2.1.x86_64.rpm                   | 420 kB  00:00     

(97/157): patch-2.7.1-8.el7.x86_64.rpm                      | 110 kB  00:00     

(98/157): openssl-libs-1.0.1e-60.el7_3.1.x86_64.rpm         | 959 kB  00:00     

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(100/157): perl-5.16.3-291 82% [=============-   ] 8.8 MB/s |  96 MB  00:02 ETA 

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(113/157): perl-Socket-2.010-4.el7.x86_64.rpm               |  49 kB  00:00     

(114/157): perl-Storable-2.45-3.el7.x86_64.rpm              |  77 kB  00:00     

(115/157): perl-Text-ParseWords-3.29-4.el7.noarch.rpm       |  14 kB  00:00     

(116/157): perl-Thread-Queue-3.02-2.el7.noarch.rpm          |  17 kB  00:00     

(118/157): perl-Time-HiRes 86% [==============-  ] 7.8 MB/s | 101 MB  00:02 ETA 

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(118/157): perl-Time-Local-1.2300-2.el7.noarch.rpm          |  24 kB  00:00     

(119/157): perl-constant-1.27-2.el7.noarch.rpm              |  19 kB  00:00     

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(127/157): perl-threads-shared-1.43-6.el7.x86_64.rpm        |  39 kB  00:00     

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(131/157): pth-2.0.7-23.el7.x86_64.rpm                      |  89 kB  00:00     

(132/157): python2-rpm-macros-3-17.el7.noarch.rpm           | 5.6 kB  00:00     

(133/157): readline-6.2-9.el7.x86_64.rpm                    | 192 kB  00:00     

(134/157): python-libs-2.7.5-48.el7.x86_64.rpm              | 5.6 MB  00:00     

(137/157): redhat-rpm-conf 92% [===============- ] 7.8 MB/s | 109 MB  00:01 ETA 

(135/157): python-rpm-macros-3-17.el7.noarch.rpm            | 6.1 kB  00:00     

(136/157): redhat-rpm-config-9.1.0-72.el7.centos.noarch.rpm |  78 kB  00:00     

(137/157): rpm-4.11.3-21.el7.x86_64.rpm                     | 1.2 MB  00:00     

(138/157): python-srpm-macros-3-17.el7.noarch.rpm           | 5.9 kB  00:00     

(139/157): rpm-build-libs-4.11.3-21.el7.x86_64.rpm          | 104 kB  00:00     

(140/157): rpm-libs-4.11.3-21.el7.x86_64.rpm                | 274 kB  00:00     

(141/157): rpm-build-4.11.3-21.el7.x86_64.rpm               | 145 kB  00:00     

(142/157): sed-4.2.2-5.el7.x86_64.rpm                       | 231 kB  00:00     

(143/157): shadow-utils-4.1.5.1-24.el7.x86_64.rpm           | 1.1 MB  00:00     

(144/157): shared-mime-info-1.1-9.el7.x86_64.rpm            | 371 kB  00:00     

(145/157): setup-2.8.71-7.el7.noarch.rpm                    | 165 kB  00:00     

(146/157): sqlite-3.7.17-8.el7.x86_64.rpm                   | 393 kB  00:00     

(147/157): unzip-6.0-16.el7.x86_64.rpm                      | 169 kB  00:00     

(148/157): ustr-1.0.4-16.el7.x86_64.rpm                     |  92 kB  00:00     

(149/157): systemd-libs-219-30.el7_3.9.x86_64.rpm           | 369 kB  00:00     

(150/157): which-2.20-7.el7.x86_64.rpm                      |  41 kB  00:00     

(151/157): xz-5.2.2-1.el7.x86_64.rpm                        | 229 kB  00:00     

(154/157): util-linux-2.23 97% [================-] 7.6 MB/s | 114 MB  00:00 ETA 

(152/157): xz-libs-5.2.2-1.el7.x86_64.rpm                   | 103 kB  00:00     

(153/157): tzdata-2017b-1.el7.noarch.rpm                    | 443 kB  00:00     

(154/157): zip-3.0-11.el7.x86_64.rpm                        | 260 kB  00:00     

(155/157): zlib-1.2.7-17.el7.x86_64.rpm                     |  90 kB  00:00     

(156/157): tar-1.26-31.el7 99% [================-] 7.5 MB/s | 116 MB  00:00 ETA 

(156/157): util-linux-2.23.2-33.el7_3.2.x86_64.rpm          | 1.9 MB  00:00     

(157/157): tar-1.26-31.el7.x86_64.rpm                       | 843 kB  00:00     
--------------------------------------------------------------------------------
Total                                              8.6 MB/s | 117 MB  00:13     
Retrieving key from file:///usr/share/distribution-gpg-keys/centos/RPM-GPG-KEY-CentOS-7
Importing GPG key 0xF4A80EB5:
 Userid     : "CentOS-7 Key (CentOS 7 Official Signing Key) <security@centos.org>"
 Fingerprint: 6341 ab27 53d7 8a78 a7c2 7bb1 24c6 a8a7 f4a8 0eb5
 From       : /usr/share/distribution-gpg-keys/centos/RPM-GPG-KEY-CentOS-7
Retrieving key from file:///usr/share/distribution-gpg-keys/epel/RPM-GPG-KEY-EPEL-7
Importing GPG key 0x352C64E5:
 Userid     : "Fedora EPEL (7) <epel@fedoraproject.org>"
 Fingerprint: 91e9 7d7c 4a5e 96f1 7f3e 888f 6a2f aea2 352c 64e5
 From       : /usr/share/distribution-gpg-keys/epel/RPM-GPG-KEY-EPEL-7
Running transaction check
Running transaction test
Transaction test succeeded
Running transaction

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  Installing : epel-rpm-macros-7-13.noarc [########################## ] 156/157
  Installing : epel-rpm-macros-7-13.noarch                              156/157 

  Installing : epel-release-7-9.noarch [                              ] 157/157
  Installing : epel-release-7-9.noarch [#                             ] 157/157
  Installing : epel-release-7-9.noarch [###                           ] 157/157
  Installing : epel-release-7-9.noarch [####                          ] 157/157
  Installing : epel-release-7-9.noarch [########                      ] 157/157
  Installing : epel-release-7-9.noarch [############################# ] 157/157
  Installing : epel-release-7-9.noarch                                  157/157 

  Verifying  : perl-HTTP-Tiny-0.033-3.el7.noarch                          1/157 

  Verifying  : nss-tools-3.28.4-1.2.el7_3.x86_64                          2/157 

  Verifying  : nss-3.28.4-1.2.el7_3.x86_64                                3/157 

  Verifying  : 1:pkgconfig-0.27.1-4.el7.x86_64                            4/157 

  Verifying  : nss-util-3.28.4-1.0.el7_3.x86_64                           5/157 

  Verifying  : redhat-rpm-config-9.1.0-72.el7.centos.noarch               6/157 

  Verifying  : glibc-2.17-157.el7_3.2.x86_64                              7/157 

  Verifying  : libgcrypt-1.5.3-13.el7_3.1.x86_64                          8/157 

  Verifying  : binutils-2.25.1-22.base.el7.x86_64                         9/157 

  Verifying  : groff-base-1.22.2-8.el7.x86_64                            10/157 

  Verifying  : perl-File-Temp-0.23.01-3.el7.noarch                       11/157 

  Verifying  : bash-4.2.46-21.el7_3.x86_64                               12/157 

  Verifying  : pcre-8.32-15.el7_2.1.x86_64                               13/157 

  Verifying  : glibc-headers-2.17-157.el7_3.2.x86_64                     14/157 

  Verifying  : file-libs-5.11-33.el7.x86_64                              15/157 

  Verifying  : patch-2.7.1-8.el7.x86_64                                  16/157 

  Verifying  : perl-Socket-2.010-4.el7.x86_64                            17/157 

  Verifying  : ca-certificates-2017.2.14-70.1.el7_3.noarch               18/157 

  Verifying  : 1:gmp-6.0.0-12.el7_1.x86_64                               19/157 

  Verifying  : elfutils-libs-0.166-2.el7.x86_64                          20/157 

  Verifying  : gawk-4.0.2-4.el7.x86_64                                   21/157 

  Verifying  : 1:make-3.82-23.el7.x86_64                                 22/157 

  Verifying  : libcurl-7.29.0-35.el7.centos.x86_64                       23/157 

  Verifying  : 4:perl-macros-5.16.3-291.el7.x86_64                       24/157 

  Verifying  : tzdata-2017b-1.el7.noarch                                 25/157 

  Verifying  : libtasn1-3.8-3.el7.x86_64                                 26/157 

  Verifying  : libuser-0.60-7.el7_1.x86_64                               27/157 

  Verifying  : epel-rpm-macros-7-13.noarch                               28/157 

  Verifying  : shared-mime-info-1.1-9.el7.x86_64                         29/157 

  Verifying  : cracklib-dicts-2.9.0-11.el7.x86_64                        30/157 

  Verifying  : libacl-2.2.51-12.el7.x86_64                               31/157 

  Verifying  : python-srpm-macros-3-17.el7.noarch                        32/157 

  Verifying  : perl-File-Path-2.09-2.el7.noarch                          33/157 

  Verifying  : readline-6.2-9.el7.x86_64                                 34/157 

  Verifying  : libffi-3.0.13-18.el7.x86_64                               35/157 

  Verifying  : grep-2.20-2.el7.x86_64                                    36/157 

  Verifying  : libassuan-2.1.0-3.el7.x86_64                              37/157 

  Verifying  : perl-Text-ParseWords-3.29-4.el7.noarch                    38/157 

  Verifying  : ustr-1.0.4-16.el7.x86_64                                  39/157 

  Verifying  : lua-5.1.4-15.el7.x86_64                                   40/157 

  Verifying  : gcc-4.8.5-11.el7.x86_64                                   41/157 

  Verifying  : sqlite-3.7.17-8.el7.x86_64                                42/157 

  Verifying  : libutempter-1.1.6-4.el7.x86_64                            43/157 

  Verifying  : cyrus-sasl-lib-2.1.26-20.el7_2.x86_64                     44/157 

  Verifying  : libidn-1.28-4.el7.x86_64                                  45/157 

  Verifying  : libmount-2.23.2-33.el7_3.2.x86_64                         46/157 

  Verifying  : epel-release-7-9.noarch                                   47/157 

  Verifying  : libdb-5.3.21-19.el7.x86_64                                48/157 

  Verifying  : 1:openssl-libs-1.0.1e-60.el7_3.1.x86_64                   49/157 

  Verifying  : unzip-6.0-16.el7.x86_64                                   50/157 

  Verifying  : util-linux-2.23.2-33.el7_3.2.x86_64                       51/157 

  Verifying  : bzip2-1.0.6-13.el7.x86_64                                 52/157 

  Verifying  : rpm-build-libs-4.11.3-21.el7.x86_64                       53/157 

  Verifying  : basesystem-10.0-7.el7.centos.noarch                       54/157 

  Verifying  : libverto-0.2.5-4.el7.x86_64                               55/157 

  Verifying  : dwz-0.11-3.el7.x86_64                                     56/157 

  Verifying  : 2:tar-1.26-31.el7.x86_64                                  57/157 

  Verifying  : gnupg2-2.0.22-4.el7.x86_64                                58/157 

  Verifying  : libpwquality-1.2.3-4.el7.x86_64                           59/157 

  Verifying  : libdb-utils-5.3.21-19.el7.x86_64                          60/157 

  Verifying  : bzip2-libs-1.0.6-13.el7.x86_64                            61/157 

  Verifying  : audit-libs-2.6.5-3.el7_3.1.x86_64                         62/157 

  Verifying  : elfutils-0.166-2.el7.x86_64                               63/157 

  Verifying  : rpm-4.11.3-21.el7.x86_64                                  64/157 

  Verifying  : python-libs-2.7.5-48.el7.x86_64                           65/157 

  Verifying  : 2:shadow-utils-4.1.5.1-24.el7.x86_64                      66/157 

  Verifying  : libmpc-1.0.1-3.el7.x86_64                                 67/157 

  Verifying  : libselinux-2.5-6.el7.x86_64                               68/157 

  Verifying  : 4:perl-libs-5.16.3-291.el7.x86_64                         69/157 

  Verifying  : libcom_err-1.42.9-9.el7.x86_64                            70/157 

  Verifying  : perl-Pod-Usage-1.63-3.el7.noarch                          71/157 

  Verifying  : cpio-2.11-24.el7.x86_64                                   72/157 

  Verifying  : glib2-2.46.2-4.el7.x86_64                                 73/157 

  Verifying  : curl-7.29.0-35.el7.centos.x86_64                          74/157 

  Verifying  : glibc-devel-2.17-157.el7_3.2.x86_64                       75/157 

  Verifying  : centos-release-7-3.1611.el7.centos.x86_64                 76/157 

  Verifying  : perl-threads-1.87-4.el7.x86_64                            77/157 

  Verifying  : gdb-7.6.1-94.el7.x86_64                                   78/157 

  Verifying  : cracklib-2.9.0-11.el7.x86_64                              79/157 

  Verifying  : libgpg-error-1.12-3.el7.x86_64                            80/157 

  Verifying  : libxml2-2.9.1-6.el7_2.3.x86_64                            81/157 

  Verifying  : libstdc++-devel-4.8.5-11.el7.x86_64                       82/157 

  Verifying  : filesystem-3.2-21.el7.x86_64                              83/157 

  Verifying  : nspr-4.13.1-1.0.el7_3.x86_64                              84/157 

  Verifying  : which-2.20-7.el7.x86_64                                   85/157 

  Verifying  : file-5.11-33.el7.x86_64                                   86/157 

  Verifying  : popt-1.13-16.el7.x86_64                                   87/157 

  Verifying  : libssh2-1.4.3-10.el7_2.1.x86_64                           88/157 

  Verifying  : libsepol-2.5-6.el7.x86_64                                 89/157 

  Verifying  : perl-threads-shared-1.43-6.el7.x86_64                     90/157 

  Verifying  : perl-Storable-2.45-3.el7.x86_64                           91/157 

  Verifying  : rpm-build-4.11.3-21.el7.x86_64                            92/157 

  Verifying  : coreutils-8.22-18.el7.x86_64                              93/157 

  Verifying  : cpp-4.8.5-11.el7.x86_64                                   94/157 

  Verifying  : 1:perl-parent-0.225-244.el7.noarch                        95/157 

  Verifying  : perl-srpm-macros-1-8.el7.noarch                           96/157 

  Verifying  : p11-kit-trust-0.20.7-3.el7.x86_64                         97/157 

  Verifying  : pam-1.1.8-18.el7.x86_64                                   98/157 

  Verifying  : gzip-1.5-8.el7.x86_64                                     99/157 

  Verifying  : perl-Encode-2.51-7.el7.x86_64                            100/157 

  Verifying  : p11-kit-0.20.7-3.el7.x86_64                              101/157 

  Verifying  : perl-Carp-1.26-244.el7.noarch                            102/157 

  Verifying  : perl-podlators-2.5.1-3.el7.noarch                        103/157 

  Verifying  : 4:perl-Time-HiRes-1.9725-3.el7.x86_64                    104/157 

  Verifying  : gdbm-1.10-8.el7.x86_64                                   105/157 

  Verifying  : libgcc-4.8.5-11.el7.x86_64                               106/157 

  Verifying  : xz-libs-5.2.2-1.el7.x86_64                               107/157 

  Verifying  : 1:findutils-4.5.11-5.el7.x86_64                          108/157 

  Verifying  : 4:perl-5.16.3-291.el7.x86_64                             109/157 

  Verifying  : mpfr-3.1.1-4.el7.x86_64                                  110/157 

  Verifying  : perl-Filter-1.49-3.el7.x86_64                            111/157 

  Verifying  : libuuid-2.23.2-33.el7_3.2.x86_64                         112/157 

  Verifying  : systemd-libs-219-30.el7_3.9.x86_64                       113/157 

  Verifying  : expat-2.1.0-10.el7_3.x86_64                              114/157 

  Verifying  : gcc-c++-4.8.5-11.el7.x86_64                              115/157 

  Verifying  : perl-Exporter-5.68-3.el7.noarch                          116/157 

  Verifying  : perl-constant-1.27-2.el7.noarch                          117/157 

  Verifying  : perl-PathTools-3.40-5.el7.x86_64                         118/157 

  Verifying  : nss-softokn-3.16.2.3-14.4.el7.x86_64                     119/157 

  Verifying  : keyutils-libs-1.5.8-3.el7.x86_64                         120/157 

  Verifying  : pinentry-0.8.1-17.el7.x86_64                             121/157 

  Verifying  : 1:perl-Pod-Escapes-1.04-291.el7.noarch                   122/157 

  Verifying  : ncurses-base-5.9-13.20130511.el7.noarch                  123/157 

  Verifying  : python2-rpm-macros-3-17.el7.noarch                       124/157 

  Verifying  : chkconfig-1.7.2-1.el7.x86_64                             125/157 

  Verifying  : pth-2.0.7-23.el7.x86_64                                  126/157 

  Verifying  : krb5-libs-1.14.1-27.el7_3.x86_64                         127/157 

  Verifying  : setup-2.8.71-7.el7.noarch                                128/157 

  Verifying  : libblkid-2.23.2-33.el7_3.2.x86_64                        129/157 

  Verifying  : perl-Thread-Queue-3.02-2.el7.noarch                      130/157 

  Verifying  : 1:perl-Pod-Simple-3.28-4.el7.noarch                      131/157 

  Verifying  : libattr-2.4.46-12.el7.x86_64                             132/157 

  Verifying  : perl-Time-Local-1.2300-2.el7.noarch                      133/157 

  Verifying  : zlib-1.2.7-17.el7.x86_64                                 134/157 

  Verifying  : perl-Pod-Perldoc-3.20-4.el7.noarch                       135/157 

  Verifying  : nss-sysinit-3.28.4-1.2.el7_3.x86_64                      136/157 

  Verifying  : libsemanage-2.5-5.1.el7_3.x86_64                         137/157 

  Verifying  : openldap-2.4.40-13.el7.x86_64                            138/157 

  Verifying  : xz-5.2.2-1.el7.x86_64                                    139/157 

  Verifying  : libcap-ng-0.7.5-4.el7.x86_64                             140/157 

  Verifying  : nss-softokn-freebl-3.16.2.3-14.4.el7.x86_64              141/157 

  Verifying  : perl-Scalar-List-Utils-1.27-248.el7.x86_64               142/157 

  Verifying  : kernel-headers-3.10.0-514.21.1.el7.x86_64                143/157 

  Verifying  : libstdc++-4.8.5-11.el7.x86_64                            144/157 

  Verifying  : sed-4.2.2-5.el7.x86_64                                   145/157 

  Verifying  : perl-Getopt-Long-2.40-2.el7.noarch                       146/157 

  Verifying  : libcap-2.22-8.el7.x86_64                                 147/157 

  Verifying  : diffutils-3.3-4.el7.x86_64                               148/157 

  Verifying  : zip-3.0-11.el7.x86_64                                    149/157 

  Verifying  : glibc-common-2.17-157.el7_3.2.x86_64                     150/157 

  Verifying  : ncurses-5.9-13.20130511.el7.x86_64                       151/157 

  Verifying  : python-rpm-macros-3-17.el7.noarch                        152/157 

  Verifying  : rpm-libs-4.11.3-21.el7.x86_64                            153/157 

  Verifying  : libgomp-4.8.5-11.el7.x86_64                              154/157 

  Verifying  : ncurses-libs-5.9-13.20130511.el7.x86_64                  155/157 

  Verifying  : info-5.1-4.el7.x86_64                                    156/157 

  Verifying  : elfutils-libelf-0.166-2.el7.x86_64                       157/157 

Installed:
  bash.x86_64 0:4.2.46-21.el7_3                                                 
  bzip2.x86_64 0:1.0.6-13.el7                                                   
  coreutils.x86_64 0:8.22-18.el7                                                
  cpio.x86_64 0:2.11-24.el7                                                     
  diffutils.x86_64 0:3.3-4.el7                                                  
  epel-release.noarch 0:7-9                                                     
  epel-rpm-macros.noarch 0:7-13                                                 
  findutils.x86_64 1:4.5.11-5.el7                                               
  gawk.x86_64 0:4.0.2-4.el7                                                     
  gcc.x86_64 0:4.8.5-11.el7                                                     
  gcc-c++.x86_64 0:4.8.5-11.el7                                                 
  grep.x86_64 0:2.20-2.el7                                                      
  gzip.x86_64 0:1.5-8.el7                                                       
  info.x86_64 0:5.1-4.el7                                                       
  make.x86_64 1:3.82-23.el7                                                     
  patch.x86_64 0:2.7.1-8.el7                                                    
  redhat-rpm-config.noarch 0:9.1.0-72.el7.centos                                
  rpm-build.x86_64 0:4.11.3-21.el7                                              
  sed.x86_64 0:4.2.2-5.el7                                                      
  shadow-utils.x86_64 2:4.1.5.1-24.el7                                          
  tar.x86_64 2:1.26-31.el7                                                      
  unzip.x86_64 0:6.0-16.el7                                                     
  util-linux.x86_64 0:2.23.2-33.el7_3.2                                         
  which.x86_64 0:2.20-7.el7                                                     
  xz.x86_64 0:5.2.2-1.el7                                                       

Dependency Installed:
  audit-libs.x86_64 0:2.6.5-3.el7_3.1                                           
  basesystem.noarch 0:10.0-7.el7.centos                                         
  binutils.x86_64 0:2.25.1-22.base.el7                                          
  bzip2-libs.x86_64 0:1.0.6-13.el7                                              
  ca-certificates.noarch 0:2017.2.14-70.1.el7_3                                 
  centos-release.x86_64 0:7-3.1611.el7.centos                                   
  chkconfig.x86_64 0:1.7.2-1.el7                                                
  cpp.x86_64 0:4.8.5-11.el7                                                     
  cracklib.x86_64 0:2.9.0-11.el7                                                
  cracklib-dicts.x86_64 0:2.9.0-11.el7                                          
  curl.x86_64 0:7.29.0-35.el7.centos                                            
  cyrus-sasl-lib.x86_64 0:2.1.26-20.el7_2                                       
  dwz.x86_64 0:0.11-3.el7                                                       
  elfutils.x86_64 0:0.166-2.el7                                                 
  elfutils-libelf.x86_64 0:0.166-2.el7                                          
  elfutils-libs.x86_64 0:0.166-2.el7                                            
  expat.x86_64 0:2.1.0-10.el7_3                                                 
  file.x86_64 0:5.11-33.el7                                                     
  file-libs.x86_64 0:5.11-33.el7                                                
  filesystem.x86_64 0:3.2-21.el7                                                
  gdb.x86_64 0:7.6.1-94.el7                                                     
  gdbm.x86_64 0:1.10-8.el7                                                      
  glib2.x86_64 0:2.46.2-4.el7                                                   
  glibc.x86_64 0:2.17-157.el7_3.2                                               
  glibc-common.x86_64 0:2.17-157.el7_3.2                                        
  glibc-devel.x86_64 0:2.17-157.el7_3.2                                         
  glibc-headers.x86_64 0:2.17-157.el7_3.2                                       
  gmp.x86_64 1:6.0.0-12.el7_1                                                   
  gnupg2.x86_64 0:2.0.22-4.el7                                                  
  groff-base.x86_64 0:1.22.2-8.el7                                              
  kernel-headers.x86_64 0:3.10.0-514.21.1.el7                                   
  keyutils-libs.x86_64 0:1.5.8-3.el7                                            
  krb5-libs.x86_64 0:1.14.1-27.el7_3                                            
  libacl.x86_64 0:2.2.51-12.el7                                                 
  libassuan.x86_64 0:2.1.0-3.el7                                                
  libattr.x86_64 0:2.4.46-12.el7                                                
  libblkid.x86_64 0:2.23.2-33.el7_3.2                                           
  libcap.x86_64 0:2.22-8.el7                                                    
  libcap-ng.x86_64 0:0.7.5-4.el7                                                
  libcom_err.x86_64 0:1.42.9-9.el7                                              
  libcurl.x86_64 0:7.29.0-35.el7.centos                                         
  libdb.x86_64 0:5.3.21-19.el7                                                  
  libdb-utils.x86_64 0:5.3.21-19.el7                                            
  libffi.x86_64 0:3.0.13-18.el7                                                 
  libgcc.x86_64 0:4.8.5-11.el7                                                  
  libgcrypt.x86_64 0:1.5.3-13.el7_3.1                                           
  libgomp.x86_64 0:4.8.5-11.el7                                                 
  libgpg-error.x86_64 0:1.12-3.el7                                              
  libidn.x86_64 0:1.28-4.el7                                                    
  libmount.x86_64 0:2.23.2-33.el7_3.2                                           
  libmpc.x86_64 0:1.0.1-3.el7                                                   
  libpwquality.x86_64 0:1.2.3-4.el7                                             
  libselinux.x86_64 0:2.5-6.el7                                                 
  libsemanage.x86_64 0:2.5-5.1.el7_3                                            
  libsepol.x86_64 0:2.5-6.el7                                                   
  libssh2.x86_64 0:1.4.3-10.el7_2.1                                             
  libstdc++.x86_64 0:4.8.5-11.el7                                               
  libstdc++-devel.x86_64 0:4.8.5-11.el7                                         
  libtasn1.x86_64 0:3.8-3.el7                                                   
  libuser.x86_64 0:0.60-7.el7_1                                                 
  libutempter.x86_64 0:1.1.6-4.el7                                              
  libuuid.x86_64 0:2.23.2-33.el7_3.2                                            
  libverto.x86_64 0:0.2.5-4.el7                                                 
  libxml2.x86_64 0:2.9.1-6.el7_2.3                                              
  lua.x86_64 0:5.1.4-15.el7                                                     
  mpfr.x86_64 0:3.1.1-4.el7                                                     
  ncurses.x86_64 0:5.9-13.20130511.el7                                          
  ncurses-base.noarch 0:5.9-13.20130511.el7                                     
  ncurses-libs.x86_64 0:5.9-13.20130511.el7                                     
  nspr.x86_64 0:4.13.1-1.0.el7_3                                                
  nss.x86_64 0:3.28.4-1.2.el7_3                                                 
  nss-softokn.x86_64 0:3.16.2.3-14.4.el7                                        
  nss-softokn-freebl.x86_64 0:3.16.2.3-14.4.el7                                 
  nss-sysinit.x86_64 0:3.28.4-1.2.el7_3                                         
  nss-tools.x86_64 0:3.28.4-1.2.el7_3                                           
  nss-util.x86_64 0:3.28.4-1.0.el7_3                                            
  openldap.x86_64 0:2.4.40-13.el7                                               
  openssl-libs.x86_64 1:1.0.1e-60.el7_3.1                                       
  p11-kit.x86_64 0:0.20.7-3.el7                                                 
  p11-kit-trust.x86_64 0:0.20.7-3.el7                                           
  pam.x86_64 0:1.1.8-18.el7                                                     
  pcre.x86_64 0:8.32-15.el7_2.1                                                 
  perl.x86_64 4:5.16.3-291.el7                                                  
  perl-Carp.noarch 0:1.26-244.el7                                               
  perl-Encode.x86_64 0:2.51-7.el7                                               
  perl-Exporter.noarch 0:5.68-3.el7                                             
  perl-File-Path.noarch 0:2.09-2.el7                                            
  perl-File-Temp.noarch 0:0.23.01-3.el7                                         
  perl-Filter.x86_64 0:1.49-3.el7                                               
  perl-Getopt-Long.noarch 0:2.40-2.el7                                          
  perl-HTTP-Tiny.noarch 0:0.033-3.el7                                           
  perl-PathTools.x86_64 0:3.40-5.el7                                            
  perl-Pod-Escapes.noarch 1:1.04-291.el7                                        
  perl-Pod-Perldoc.noarch 0:3.20-4.el7                                          
  perl-Pod-Simple.noarch 1:3.28-4.el7                                           
  perl-Pod-Usage.noarch 0:1.63-3.el7                                            
  perl-Scalar-List-Utils.x86_64 0:1.27-248.el7                                  
  perl-Socket.x86_64 0:2.010-4.el7                                              
  perl-Storable.x86_64 0:2.45-3.el7                                             
  perl-Text-ParseWords.noarch 0:3.29-4.el7                                      
  perl-Thread-Queue.noarch 0:3.02-2.el7                                         
  perl-Time-HiRes.x86_64 4:1.9725-3.el7                                         
  perl-Time-Local.noarch 0:1.2300-2.el7                                         
  perl-constant.noarch 0:1.27-2.el7                                             
  perl-libs.x86_64 4:5.16.3-291.el7                                             
  perl-macros.x86_64 4:5.16.3-291.el7                                           
  perl-parent.noarch 1:0.225-244.el7                                            
  perl-podlators.noarch 0:2.5.1-3.el7                                           
  perl-srpm-macros.noarch 0:1-8.el7                                             
  perl-threads.x86_64 0:1.87-4.el7                                              
  perl-threads-shared.x86_64 0:1.43-6.el7                                       
  pinentry.x86_64 0:0.8.1-17.el7                                                
  pkgconfig.x86_64 1:0.27.1-4.el7                                               
  popt.x86_64 0:1.13-16.el7                                                     
  pth.x86_64 0:2.0.7-23.el7                                                     
  python-libs.x86_64 0:2.7.5-48.el7                                             
  python-rpm-macros.noarch 0:3-17.el7                                           
  python-srpm-macros.noarch 0:3-17.el7                                          
  python2-rpm-macros.noarch 0:3-17.el7                                          
  readline.x86_64 0:6.2-9.el7                                                   
  rpm.x86_64 0:4.11.3-21.el7                                                    
  rpm-build-libs.x86_64 0:4.11.3-21.el7                                         
  rpm-libs.x86_64 0:4.11.3-21.el7                                               
  setup.noarch 0:2.8.71-7.el7                                                   
  shared-mime-info.x86_64 0:1.1-9.el7                                           
  sqlite.x86_64 0:3.7.17-8.el7                                                  
  systemd-libs.x86_64 0:219-30.el7_3.9                                          
  tzdata.noarch 0:2017b-1.el7                                                   
  ustr.x86_64 0:1.0.4-16.el7                                                    
  xz-libs.x86_64 0:5.2.2-1.el7                                                  
  zip.x86_64 0:3.0-11.el7                                                       
  zlib.x86_64 0:1.2.7-17.el7                                                    

Complete!
Finish: yum install
Start: creating root cache
Finish: creating root cache
Finish: chroot init
INFO: Installed packages:
Start: buildsrpm
Start: rpmbuild -bs
warning: Could not canonicalize hostname: fdf83fff02394b6a803e864d2a14838c
Building target platforms: x86_64
Building for target x86_64
Wrote: /builddir/build/SRPMS/gap-pkg-automata-1.13-0.3.el7.centos.src.rpm
Finish: rpmbuild -bs
Finish: buildsrpm
INFO: Done(gap-pkg-automata.spec) Config(child) 0 minutes 58 seconds
INFO: Results and/or logs in: intermediate-srpm
Finish: run
INFO: unmounting tmpfs.
WARNING: Could not find required logging config file: /var/lib/copr-rpmbuild/results/configs/logging.ini. Using default...
INFO: mock.py version 1.4.2 starting (python version = 3.6.1)...
Start: init plugins
INFO: tmpfs initialized
INFO: selinux disabled
INFO: compress_logs: initialized
Finish: init plugins
Start: run
INFO: Start(intermediate-srpm/gap-pkg-automata-1.13-0.3.el7.centos.src.rpm)  Config(565363-epel-7-x86_64)
Start: chroot init
INFO: mounting tmpfs at /var/lib/mock/565363-epel-7-x86_64/root.
INFO: calling preinit hooks
INFO: enabled root cache
Start: unpacking root cache
Finish: unpacking root cache
INFO: enabled HW Info plugin
Mock Version: 1.4.2
INFO: Mock Version: 1.4.2
Finish: chroot init
Start: build phase for gap-pkg-automata-1.13-0.3.el7.centos.src.rpm
Start: build setup for gap-pkg-automata-1.13-0.3.el7.centos.src.rpm
warning: Could not canonicalize hostname: 65dd79edbcf44a85ba122a715f50e52b
Building target platforms: x86_64
Building for target x86_64
Wrote: /builddir/build/SRPMS/gap-pkg-automata-1.13-0.3.el7.centos.src.rpm

Yum-utils package has been deprecated, use dnf instead.
See 'man yum2dnf' for more information.



copr_base                                                   | 3.5 kB  00:00     

base                                                        | 3.6 kB  00:00     

epel                                                        | 4.3 kB  00:00     

extras                                                      | 3.4 kB  00:00     

updates                                                     | 3.4 kB  00:00     

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(4/5): epel/primary_db      5% [-                ]  0.0 B/s | 834 kB  --:-- ETA 

(4/5): epel/primary_db     18% [===              ] 2.4 MB/s | 3.0 MB  00:05 ETA 

(3/5): epel/primary_db                                      | 4.8 MB  00:00     

(5/5): updates/primary_db  61% [==========-      ] 3.7 MB/s |  10 MB  00:01 ETA 

(5/5): updates/primary_db  74% [============-    ] 3.8 MB/s |  12 MB  00:01 ETA 

(4/5): updates/primary_db                                   | 5.7 MB  00:01     

(5/5): base/primary_db     91% [===============  ] 4.0 MB/s |  15 MB  00:00 ETA 

(5/5): base/primary_db     97% [================-] 4.0 MB/s |  16 MB  00:00 ETA 

(5/5): base/primary_db                                      | 5.6 MB  00:02     
Getting requirements for gap-pkg-automata-1.13-0.3.el7.centos.src
 --> gap-devel-4.8.7-0.12.el7.centos.x86_64
 --> GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Running transaction check
---> Package GAPDoc-latex.noarch 0:1.5.1-0.12.el7.centos will be installed
--> Processing Dependency: gap-online-help for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: ghostscript for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex(a4wide.sty) for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex(color.cfg) for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex(english.ldf) for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex(enumitem.sty) for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex(fancyvrb.sty) for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex(language.dat) for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex(pslatex.sty) for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex(psnfss.map) for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex(updmap-hdr.cfg) for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex-bibtex for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex-cm for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex-cm-super for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex-dvips for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex-ec for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex-gsftopk for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex-helvetic for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex-latex-bin for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex-makeindex for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex-mfware for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex-rsfs for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex-symbol for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
--> Processing Dependency: tex-times for package: GAPDoc-latex-1.5.1-0.12.el7.centos.noarch
---> Package gap-devel.x86_64 0:4.8.7-0.12.el7.centos will be installed
--> Processing Dependency: gap-core = 4.8.7-0.12.el7.centos for package: gap-devel-4.8.7-0.12.el7.centos.x86_64
--> Processing Dependency: gmp-devel(x86-64) for package: gap-devel-4.8.7-0.12.el7.centos.x86_64
--> Running transaction check
---> Package gap-core.x86_64 0:4.8.7-0.12.el7.centos will be installed
--> Processing Dependency: gap-libs = 4.8.7-0.12.el7.centos for package: gap-core-4.8.7-0.12.el7.centos.x86_64
--> Processing Dependency: GAPDoc for package: gap-core-4.8.7-0.12.el7.centos.x86_64
--> Processing Dependency: hicolor-icon-theme for package: gap-core-4.8.7-0.12.el7.centos.x86_64
---> Package gap-online-help.noarch 0:4.8.7-0.12.el7.centos will be installed
---> Package ghostscript.x86_64 0:9.07-20.el7_3.5 will be installed
--> Processing Dependency: urw-fonts >= 1.1 for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: poppler-data for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libtiff.so.5(LIBTIFF_4.0)(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libpng15.so.15(PNG15_0)(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libjpeg.so.62(LIBJPEG_6.2)(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: ghostscript-fonts for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libtiff.so.5()(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libpng15.so.15()(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: liblcms2.so.2()(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libjpeg.so.62()(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libfreetype.so.6()(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libfontconfig.so.1()(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libcupsimage.so.2()(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libcups.so.2()(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libXt.so.6()(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libXext.so.6()(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libX11.so.6()(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libSM.so.6()(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
--> Processing Dependency: libICE.so.6()(64bit) for package: ghostscript-9.07-20.el7_3.5.x86_64
---> Package gmp-devel.x86_64 1:6.0.0-12.el7_1 will be installed
---> Package texlive-a4wide.noarch 0:svn20943.0-52.el7 will be installed
--> Processing Dependency: texlive-kpathsea-bin for package: texlive-a4wide-svn20943.0-52.el7.noarch
--> Processing Dependency: texlive-base for package: texlive-a4wide-svn20943.0-52.el7.noarch
--> Processing Dependency: tex-kpathsea for package: texlive-a4wide-svn20943.0-52.el7.noarch
--> Processing Dependency: tex(a4.sty) for package: texlive-a4wide-svn20943.0-52.el7.noarch
---> Package texlive-babel.noarch 2:svn24756.3.8m-38.el7 will be installed
--> Processing Dependency: tex(scalefnt.sty) for package: 2:texlive-babel-svn24756.3.8m-38.el7.noarch
--> Processing Dependency: tex(keyval.sty) for package: 2:texlive-babel-svn24756.3.8m-38.el7.noarch
--> Processing Dependency: tex(inputenc.sty) for package: 2:texlive-babel-svn24756.3.8m-38.el7.noarch
---> Package texlive-bibtex.noarch 2:svn26689.0.99d-38.el7 will be installed
--> Processing Dependency: texlive-bibtex-bin for package: 2:texlive-bibtex-svn26689.0.99d-38.el7.noarch
---> Package texlive-cm.noarch 2:svn29581.0-38.el7 will be installed
--> Processing Dependency: texlive-tetex-bin for package: 2:texlive-cm-svn29581.0-38.el7.noarch
--> Processing Dependency: texlive-tetex-bin for package: 2:texlive-cm-svn29581.0-38.el7.noarch
--> Processing Dependency: tex-tetex for package: 2:texlive-cm-svn29581.0-38.el7.noarch
--> Processing Dependency: tex-tetex for package: 2:texlive-cm-svn29581.0-38.el7.noarch
---> Package texlive-cm-super.noarch 2:svn15878.0-38.el7 will be installed
---> Package texlive-dvips.noarch 2:svn29585.0-38.el7 will be installed
--> Processing Dependency: texlive-latex-fonts for package: 2:texlive-dvips-svn29585.0-38.el7.noarch
--> Processing Dependency: texlive-dvips-bin for package: 2:texlive-dvips-svn29585.0-38.el7.noarch
---> Package texlive-ec.noarch 2:svn25033.1.0-38.el7 will be installed
---> Package texlive-enumitem.noarch 2:svn24146.3.5.2-38.el7 will be installed
---> Package texlive-fancyvrb.noarch 2:svn18492.2.8-38.el7 will be installed
--> Processing Dependency: tex(pstricks.sty) for package: 2:texlive-fancyvrb-svn18492.2.8-38.el7.noarch
---> Package texlive-gsftopk.noarch 2:svn26689.1.19.2-38.el7 will be installed
--> Processing Dependency: texlive-gsftopk-bin for package: 2:texlive-gsftopk-svn26689.1.19.2-38.el7.noarch
---> Package texlive-helvetic.noarch 2:svn28614.0-38.el7 will be installed
---> Package texlive-hyphen-base.noarch 2:svn29197.0-38.el7 will be installed
---> Package texlive-latex-bin.noarch 2:svn26689.0-38.el7 will be installed
--> Processing Dependency: texlive-latex-bin-bin for package: 2:texlive-latex-bin-svn26689.0-38.el7.noarch
---> Package texlive-latexconfig.noarch 2:svn28991.0-38.el7 will be installed
---> Package texlive-makeindex.noarch 2:svn26689.2.12-38.el7 will be installed
--> Processing Dependency: texlive-makeindex-bin for package: 2:texlive-makeindex-svn26689.2.12-38.el7.noarch
---> Package texlive-mfware.noarch 2:svn26689.0-38.el7 will be installed
--> Processing Dependency: texlive-mfware-bin for package: 2:texlive-mfware-svn26689.0-38.el7.noarch
---> Package texlive-pslatex.noarch 2:svn16416.0-38.el7 will be installed
---> Package texlive-psnfss.noarch 2:svn23394.9.2a-38.el7 will be installed
---> Package texlive-rsfs.noarch 2:svn15878.0-38.el7 will be installed
---> Package texlive-symbol.noarch 2:svn28614.0-38.el7 will be installed
---> Package texlive-texlive.infra.noarch 2:svn28217.0-38.el7 will be installed
--> Processing Dependency: texlive-texlive.infra-bin for package: 2:texlive-texlive.infra-svn28217.0-38.el7.noarch
---> Package texlive-times.noarch 2:svn28614.0-38.el7 will be installed
--> Running transaction check
---> Package GAPDoc.noarch 0:1.5.1-0.12.el7.centos will be installed
---> Package cups-libs.x86_64 1:1.6.3-26.el7 will be installed
--> Processing Dependency: libavahi-common.so.3()(64bit) for package: 1:cups-libs-1.6.3-26.el7.x86_64
--> Processing Dependency: libavahi-client.so.3()(64bit) for package: 1:cups-libs-1.6.3-26.el7.x86_64
---> Package fontconfig.x86_64 0:2.10.95-10.el7 will be installed
--> Processing Dependency: fontpackages-filesystem for package: fontconfig-2.10.95-10.el7.x86_64
---> Package freetype.x86_64 0:2.4.11-12.el7 will be installed
---> Package gap-libs.noarch 0:4.8.7-0.12.el7.centos will be installed
---> Package ghostscript-fonts.noarch 0:5.50-32.el7 will be installed
--> Processing Dependency: xorg-x11-font-utils for package: ghostscript-fonts-5.50-32.el7.noarch
---> Package hicolor-icon-theme.noarch 0:0.12-7.el7 will be installed
---> Package lcms2.x86_64 0:2.6-3.el7 will be installed
---> Package libICE.x86_64 0:1.0.9-2.el7 will be installed
---> Package libSM.x86_64 0:1.2.2-2.el7 will be installed
---> Package libX11.x86_64 0:1.6.3-3.el7 will be installed
--> Processing Dependency: libX11-common >= 1.6.3-3.el7 for package: libX11-1.6.3-3.el7.x86_64
--> Processing Dependency: libxcb.so.1()(64bit) for package: libX11-1.6.3-3.el7.x86_64
---> Package libXext.x86_64 0:1.3.3-3.el7 will be installed
---> Package libXt.x86_64 0:1.1.4-6.1.el7 will be installed
---> Package libjpeg-turbo.x86_64 0:1.2.90-5.el7 will be installed
---> Package libpng.x86_64 2:1.5.13-7.el7_2 will be installed
---> Package libtiff.x86_64 0:4.0.3-27.el7_3 will be installed
--> Processing Dependency: libjbig.so.2.0()(64bit) for package: libtiff-4.0.3-27.el7_3.x86_64
---> Package poppler-data.noarch 0:0.4.6-3.el7 will be installed
---> Package texlive-base.noarch 2:2012-38.20130427_r30134.el7 will be installed
---> Package texlive-bibtex-bin.x86_64 2:svn26509.0-38.20130427_r30134.el7 will be installed
--> Processing Dependency: texlive-kpathsea-lib = 2:2012-38.20130427_r30134.el7 for package: 2:texlive-bibtex-bin-svn26509.0-38.20130427_r30134.el7.x86_64
--> Processing Dependency: libkpathsea.so.6()(64bit) for package: 2:texlive-bibtex-bin-svn26509.0-38.20130427_r30134.el7.x86_64
---> Package texlive-carlisle.noarch 2:svn18258.0-38.el7 will be installed
--> Processing Dependency: tex(tabularx.sty) for package: 2:texlive-carlisle-svn18258.0-38.el7.noarch
--> Processing Dependency: tex(longtable.sty) for package: 2:texlive-carlisle-svn18258.0-38.el7.noarch
---> Package texlive-dvips-bin.x86_64 2:svn26509.0-38.20130427_r30134.el7 will be installed
---> Package texlive-graphics.noarch 2:svn25405.1.0o-38.el7 will be installed
---> Package texlive-gsftopk-bin.x86_64 2:svn26509.0-38.20130427_r30134.el7 will be installed
---> Package texlive-kpathsea.noarch 2:svn28792.0-38.el7 will be installed
---> Package texlive-kpathsea-bin.x86_64 2:svn27347.0-38.20130427_r30134.el7 will be installed
---> Package texlive-latex.noarch 2:svn27907.0-38.el7 will be installed
--> Processing Dependency: tex-pdftex for package: 2:texlive-latex-svn27907.0-38.el7.noarch
--> Processing Dependency: tex-luatex for package: 2:texlive-latex-svn27907.0-38.el7.noarch
--> Processing Dependency: tex(url.sty) for package: 2:texlive-latex-svn27907.0-38.el7.noarch
--> Processing Dependency: tex(hyperref.sty) for package: 2:texlive-latex-svn27907.0-38.el7.noarch
---> Package texlive-latex-bin-bin.noarch 2:svn14050.0-38.20130427_r30134.el7 will be installed
---> Package texlive-latex-fonts.noarch 2:svn28888.0-38.el7 will be installed
---> Package texlive-makeindex-bin.x86_64 2:svn26509.0-38.20130427_r30134.el7 will be installed
---> Package texlive-mfware-bin.x86_64 2:svn26509.0-38.20130427_r30134.el7 will be installed
---> Package texlive-ntgclass.noarch 2:svn15878.0-38.el7 will be installed
---> Package texlive-pstricks.noarch 2:svn29678.2.39-38.el7 will be installed
--> Processing Dependency: tex(xkvview.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
--> Processing Dependency: tex(xkeyval.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
--> Processing Dependency: tex(xcolor.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
--> Processing Dependency: tex(subfig.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
--> Processing Dependency: tex(showexpl.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
--> Processing Dependency: tex(setspace.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
--> Processing Dependency: tex(scrpage2.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
--> Processing Dependency: tex(ragged2e.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
--> Processing Dependency: tex(pstricks-add.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
--> Processing Dependency: tex(pst-xkey.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
--> Processing Dependency: tex(pst-tree.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
--> Processing Dependency: tex(pst-text.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
--> Processing Dependency: tex(pst-plot.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
--> Processing Dependency: tex(pst-node.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
--> Processing Dependency: tex(pst-grad.sty) for package: 2:texlive-pstricks-svn29678.2.39-38.el7.noarch
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--> Processing Dependency: mesa-libglapi = 11.2.2-2.20160614.el7 for package: mesa-libGL-11.2.2-2.20160614.el7.x86_64
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--> Processing Dependency: udev for package: libdrm-2.4.67-3.el7.x86_64
--> Processing Dependency: libpciaccess.so.0()(64bit) for package: libdrm-2.4.67-3.el7.x86_64
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--> Processing Dependency: hardlink for package: dracut-033-463.el7_3.1.x86_64
--> Running transaction check
---> Package device-mapper.x86_64 7:1.02.135-1.el7_3.4 will be installed
---> Package hardlink.x86_64 1:1.0-19.el7 will be installed
---> Package kpartx.x86_64 0:0.4.9-99.el7_3.3 will be installed
---> Package procps-ng.x86_64 0:3.3.10-10.el7 will be installed
--> Finished Dependency Resolution

Dependencies Resolved

================================================================================
 Package               Arch   Version                             Repository
                                                                           Size
================================================================================
Installing:
 GAPDoc-latex          noarch 1.5.1-0.12.el7.centos               copr_base
                                                                          4.6 k
 gap-devel             x86_64 4.8.7-0.12.el7.centos               copr_base
                                                                          527 k
Installing for dependencies:
 GAPDoc                noarch 1.5.1-0.12.el7.centos               copr_base
                                                                          1.3 M
 acl                   x86_64 2.2.51-12.el7                       base     81 k
 avahi-libs            x86_64 0.6.31-17.el7                       base     61 k
 cairo                 x86_64 1.14.2-1.el7                        base    711 k
 cryptsetup-libs       x86_64 1.7.2-1.el7                         base    216 k
 cups-libs             x86_64 1:1.6.3-26.el7                      base    356 k
 dbus                  x86_64 1:1.6.12-17.el7                     base    307 k
 dbus-libs             x86_64 1:1.6.12-17.el7                     base    151 k
 device-mapper         x86_64 7:1.02.135-1.el7_3.4                updates 269 k
 device-mapper-libs    x86_64 7:1.02.135-1.el7_3.4                updates 333 k
 dracut                x86_64 033-463.el7_3.1                     updates 317 k
 fontconfig            x86_64 2.10.95-10.el7                      base    229 k
 fontpackages-filesystem
                       noarch 1.44-8.el7                          base    9.9 k
 freetype              x86_64 2.4.11-12.el7                       base    391 k
 gap-core              x86_64 4.8.7-0.12.el7.centos               copr_base
                                                                          2.7 M
 gap-libs              noarch 4.8.7-0.12.el7.centos               copr_base
                                                                           34 M
 gap-online-help       noarch 4.8.7-0.12.el7.centos               copr_base
                                                                          8.7 M
 ghostscript           x86_64 9.07-20.el7_3.5                     updates 4.3 M
 ghostscript-fonts     noarch 5.50-32.el7                         base    324 k
 gmp-devel             x86_64 1:6.0.0-12.el7_1                    base    181 k
 hardlink              x86_64 1:1.0-19.el7                        base     14 k
 hicolor-icon-theme    noarch 0.12-7.el7                          base     42 k
 hwdata                x86_64 0.252-8.4.el7                       base    2.1 M
 jbigkit-libs          x86_64 2.0-11.el7                          base     46 k
 kmod                  x86_64 20-9.el7                            base    115 k
 kmod-libs             x86_64 20-9.el7                            base     47 k
 kpartx                x86_64 0.4.9-99.el7_3.3                    updates  68 k
 lcms2                 x86_64 2.6-3.el7                           base    150 k
 libICE                x86_64 1.0.9-2.el7                         base     65 k
 libSM                 x86_64 1.2.2-2.el7                         base     39 k
 libX11                x86_64 1.6.3-3.el7                         base    606 k
 libX11-common         noarch 1.6.3-3.el7                         base    162 k
 libXau                x86_64 1.0.8-2.1.el7                       base     29 k
 libXdamage            x86_64 1.1.4-4.1.el7                       base     20 k
 libXext               x86_64 1.3.3-3.el7                         base     39 k
 libXfixes             x86_64 5.0.1-2.1.el7                       base     18 k
 libXfont              x86_64 1.5.1-2.el7                         base    150 k
 libXrender            x86_64 0.9.8-2.1.el7                       base     25 k
 libXt                 x86_64 1.1.4-6.1.el7                       base    173 k
 libXxf86vm            x86_64 1.1.3-2.1.el7                       base     17 k
 libdrm                x86_64 2.4.67-3.el7                        base    141 k
 libfontenc            x86_64 1.1.2-3.el7                         base     30 k
 libjpeg-turbo         x86_64 1.2.90-5.el7                        base    134 k
 libpciaccess          x86_64 0.13.4-3.el7_3                      updates  26 k
 libpng                x86_64 2:1.5.13-7.el7_2                    base    213 k
 libtiff               x86_64 4.0.3-27.el7_3                      updates 170 k
 libxcb                x86_64 1.11-4.el7                          base    189 k
 libxshmfence          x86_64 1.2-1.el7                           base    7.2 k
 mesa-libEGL           x86_64 11.2.2-2.20160614.el7               base     85 k
 mesa-libGL            x86_64 11.2.2-2.20160614.el7               base    162 k
 mesa-libgbm           x86_64 11.2.2-2.20160614.el7               base     42 k
 mesa-libglapi         x86_64 11.2.2-2.20160614.el7               base     40 k
 openjpeg-libs         x86_64 1.5.1-16.el7_3                      updates  86 k
 pixman                x86_64 0.34.0-1.el7                        base    248 k
 poppler               x86_64 0.26.5-16.el7                       base    783 k
 poppler-data          noarch 0.4.6-3.el7                         base    2.2 M
 procps-ng             x86_64 3.3.10-10.el7                       base    288 k
 qrencode-libs         x86_64 3.4.1-3.el7                         base     50 k
 systemd               x86_64 219-30.el7_3.9                      updates 5.2 M
 texlive-a4wide        noarch svn20943.0-52.el7                   epel     11 k
 texlive-algorithms    noarch 2:svn15878.0.1-38.el7               base     21 k
 texlive-amsfonts      noarch 2:svn29208.3.04-38.el7              base    3.6 M
 texlive-amsmath       noarch 2:svn29327.2.14-38.el7              base     49 k
 texlive-attachfile    noarch 2:svn21866.v1.5b-38.el7             base     21 k
 texlive-babel         noarch 2:svn24756.3.8m-38.el7              base    129 k
 texlive-babelbib      noarch 2:svn25245.1.31-38.el7              base     49 k
 texlive-base          noarch 2:2012-38.20130427_r30134.el7       base    325 k
 texlive-bera          noarch 2:svn20031.0-38.el7                 base    347 k
 texlive-bibtex        noarch 2:svn26689.0.99d-38.el7             base     33 k
 texlive-bibtex-bin    x86_64 2:svn26509.0-38.20130427_r30134.el7 base     65 k
 texlive-booktabs      noarch 2:svn15878.1.61803-38.el7           base     19 k
 texlive-breakurl      noarch 2:svn15878.1.30-38.el7              base     20 k
 texlive-caption       noarch 2:svn29026.3.3__2013_02_03_-38.el7  base     51 k
 texlive-carlisle      noarch 2:svn18258.0-38.el7                 base     29 k
 texlive-chngcntr      noarch 2:svn17157.1.0a-38.el7              base     19 k
 texlive-cm            noarch 2:svn29581.0-38.el7                 base    291 k
 texlive-cm-super      noarch 2:svn15878.0-38.el7                 base     62 M
 texlive-colortbl      noarch 2:svn25394.v1.0a-38.el7             base     20 k
 texlive-csquotes      noarch 2:svn24393.5.1d-38.el7              base     36 k
 texlive-currfile      noarch 2:svn29012.0.7b-38.el7              base     21 k
 texlive-dvips         noarch 2:svn29585.0-38.el7                 base    217 k
 texlive-dvips-bin     x86_64 2:svn26509.0-38.20130427_r30134.el7 base    129 k
 texlive-ec            noarch 2:svn25033.1.0-38.el7               base    467 k
 texlive-enumitem      noarch 2:svn24146.3.5.2-38.el7             base     29 k
 texlive-eso-pic       noarch 2:svn21515.2.0c-38.el7              base     21 k
 texlive-etex-pkg      noarch 2:svn15878.2.0-38.el7               base     22 k
 texlive-etoolbox      noarch 2:svn20922.2.1-38.el7               base     25 k
 texlive-fancyvrb      noarch 2:svn18492.2.8-38.el7               base     30 k
 texlive-filecontents  noarch 2:svn24250.1.3-38.el7               base     19 k
 texlive-filehook      noarch 2:svn24280.0.5d-38.el7              base     22 k
 texlive-float         noarch 2:svn15878.1.3d-38.el7              base     20 k
 texlive-fontspec      noarch 2:svn29412.v2.3a-38.el7             base     38 k
 texlive-footmisc      noarch 2:svn23330.5.5b-38.el7              base     23 k
 texlive-fp            noarch 2:svn15878.0-38.el7                 base     39 k
 texlive-geometry      noarch 2:svn19716.5.6-38.el7               base     26 k
 texlive-graphics      noarch 2:svn25405.1.0o-38.el7              base     33 k
 texlive-gsftopk       noarch 2:svn26689.1.19.2-38.el7            base     24 k
 texlive-gsftopk-bin   x86_64 2:svn26509.0-38.20130427_r30134.el7 base     30 k
 texlive-helvetic      noarch 2:svn28614.0-38.el7                 base    614 k
 texlive-hyperref      noarch 2:svn28213.6.83m-38.el7             base    139 k
 texlive-hyphen-base   noarch 2:svn29197.0-38.el7                 base     39 k
 texlive-ifetex        noarch 2:svn24853.1.2-38.el7               base     18 k
 texlive-ifxetex       noarch 2:svn19685.0.5-38.el7               base     18 k
 texlive-index         noarch 2:svn24099.4.1beta-38.el7           base     29 k
 texlive-kastrup       noarch 2:svn15878.0-38.el7                 base     18 k
 texlive-koma-script   noarch 2:svn27255.3.11b-38.el7             base    5.1 M
 texlive-kpathsea      noarch 2:svn28792.0-38.el7                 base    140 k
 texlive-kpathsea-bin  x86_64 2:svn27347.0-38.20130427_r30134.el7 base     40 k
 texlive-kpathsea-lib  x86_64 2:2012-38.20130427_r30134.el7       base     78 k
 texlive-l3kernel      noarch 2:svn29409.SVN_4469-38.el7          base    107 k
 texlive-l3packages    noarch 2:svn29361.SVN_4467-38.el7          base     36 k
 texlive-latex         noarch 2:svn27907.0-38.el7                 base    197 k
 texlive-latex-bin     noarch 2:svn26689.0-38.el7                 base     20 k
 texlive-latex-bin-bin noarch 2:svn14050.0-38.20130427_r30134.el7 base     17 k
 texlive-latex-fonts   noarch 2:svn28888.0-38.el7                 base     42 k
 texlive-latexconfig   noarch 2:svn28991.0-38.el7                 base     26 k
 texlive-listings      noarch 2:svn15878.1.4-38.el7               base    138 k
 texlive-lm            noarch 2:svn28119.2.004-38.el7             base     13 M
 texlive-lualatex-math noarch 2:svn29346.1.2-38.el7               base     21 k
 texlive-luaotfload    noarch 2:svn26718.1.26-38.el7              base    101 k
 texlive-luaotfload-bin
                       noarch 2:svn18579.0-38.20130427_r30134.el7 base     17 k
 texlive-luatex        noarch 2:svn26689.0.70.1-38.el7            base     37 k
 texlive-luatex-bin    x86_64 2:svn26912.0-38.20130427_r30134.el7 base    1.7 M
 texlive-luatexbase    noarch 2:svn22560.0.31-38.el7              base     27 k
 texlive-makeindex     noarch 2:svn26689.2.12-38.el7              base     30 k
 texlive-makeindex-bin x86_64 2:svn26509.0-38.20130427_r30134.el7 base     38 k
 texlive-marginnote    noarch 2:svn25880.v1.1i-38.el7             base     20 k
 texlive-memoir        noarch 2:svn21638.3.6j_patch_6.0g-38.el7   base     97 k
 texlive-mfware        noarch 2:svn26689.0-38.el7                 base     31 k
 texlive-mfware-bin    x86_64 2:svn26509.0-38.20130427_r30134.el7 base     89 k
 texlive-mparhack      noarch 2:svn15878.1.4-38.el7               base     20 k
 texlive-ms            noarch 2:svn24467.0-38.el7                 base     24 k
 texlive-multido       noarch 2:svn18302.1.42-38.el7              base     21 k
 texlive-ntgclass      noarch 2:svn15878.0-38.el7                 base     35 k
 texlive-oberdiek      noarch 2:svn26725.0-38.el7                 base    307 k
 texlive-paralist      noarch 2:svn15878.2.3b-38.el7              base     21 k
 texlive-parallel      noarch 2:svn15878.0-38.el7                 base     21 k
 texlive-pdftex        noarch 2:svn29585.1.40.11-38.el7           base    140 k
 texlive-pdftex-bin    x86_64 2:svn27321.0-38.20130427_r30134.el7 base    360 k
 texlive-pgf           noarch 2:svn22614.2.10-38.el7              base    468 k
 texlive-pslatex       noarch 2:svn16416.0-38.el7                 base     24 k
 texlive-psnfss        noarch 2:svn23394.9.2a-38.el7              base     45 k
 texlive-pst-3d        noarch 2:svn17257.1.10-38.el7              base     21 k
 texlive-pst-coil      noarch 2:svn24020.1.06-38.el7              base     21 k
 texlive-pst-eps       noarch 2:svn15878.1.0-38.el7               base     20 k
 texlive-pst-fill      noarch 2:svn15878.1.01-38.el7              base     21 k
 texlive-pst-grad      noarch 2:svn15878.1.06-38.el7              base     21 k
 texlive-pst-math      noarch 2:svn20176.0.61-38.el7              base     22 k
 texlive-pst-node      noarch 2:svn27799.1.25-38.el7              base     40 k
 texlive-pst-plot      noarch 2:svn28729.1.44-38.el7              base     36 k
 texlive-pst-text      noarch 2:svn15878.1.00-38.el7              base     21 k
 texlive-pst-tree      noarch 2:svn24142.1.12-38.el7              base     24 k
 texlive-pstricks      noarch 2:svn29678.2.39-38.el7              base     97 k
 texlive-pstricks-add  noarch 2:svn28750.3.59-38.el7              base     41 k
 texlive-qstest        noarch 2:svn15878.0-38.el7                 base     22 k
 texlive-rsfs          noarch 2:svn15878.0-38.el7                 base     75 k
 texlive-sauerj        noarch 2:svn15878.0-38.el7                 base     23 k
 texlive-setspace      noarch 2:svn24881.6.7a-38.el7              base     24 k
 texlive-showexpl      noarch 2:svn27790.v0.3j-38.el7             base     21 k
 texlive-soul          noarch 2:svn15878.2.4-38.el7               base     23 k
 texlive-subfig        noarch 2:svn15878.1.3-38.el7               base     24 k
 texlive-symbol        noarch 2:svn28614.0-38.el7                 base     55 k
 texlive-tetex         noarch 2:svn29585.3.0-38.el7               base     88 k
 texlive-tetex-bin     noarch 2:svn27344.0-38.20130427_r30134.el7 base     18 k
 texlive-texlive.infra noarch 2:svn28217.0-38.el7                 base    137 k
 texlive-texlive.infra-bin
                       x86_64 2:svn22566.0-38.20130427_r30134.el7 base     16 k
 texlive-thumbpdf      noarch 2:svn26689.3.15-38.el7              base     38 k
 texlive-thumbpdf-bin  noarch 2:svn6898.0-38.20130427_r30134.el7  base     17 k
 texlive-times         noarch 2:svn28614.0-38.el7                 base    388 k
 texlive-tipa          noarch 2:svn29349.1.3-38.el7               base    2.8 M
 texlive-tools         noarch 2:svn26263.0-38.el7                 base     62 k
 texlive-underscore    noarch 2:svn18261.0-38.el7                 base     22 k
 texlive-unicode-math  noarch 2:svn29413.0.7d-38.el7              base     61 k
 texlive-url           noarch 2:svn16864.3.2-38.el7               base     26 k
 texlive-varwidth      noarch 2:svn24104.0.92-38.el7              base     21 k
 texlive-xcolor        noarch 2:svn15878.2.11-38.el7              base     35 k
 texlive-xkeyval       noarch 2:svn27995.2.6a-38.el7              base     27 k
 texlive-xunicode      noarch 2:svn23897.0.981-38.el7             base     44 k
 urw-fonts             noarch 2.4-16.el7                          base    3.0 M
 xorg-x11-font-utils   x86_64 1:7.5-20.el7                        base     87 k
 zziplib               x86_64 0.13.62-5.el7                       base     81 k

Transaction Summary
================================================================================
Install  2 Packages (+181 Dependent packages)

Total download size: 169 M
Installed size: 347 M
Downloading packages:

(1/183): GAPDoc-latex-1.5.1-0.12.el7.centos.noarch.rpm      | 4.6 kB  00:00     

(2/183): GAPDoc-1.5.1-0.12.el7.centos.noarch.rpm            | 1.3 MB  00:00     

(3/183): acl-2.2.51-12.el7.x86_64.rpm                       |  81 kB  00:00     

(4/183): avahi-libs-0.6.31-17.el7.x86_64.rpm                |  61 kB  00:00     

(5/183): cryptsetup-libs-1.7.2-1.el7.x86_64.rpm             | 216 kB  00:00     

(6/183): cairo-1.14.2-1.el7.x86_64.rpm                      | 711 kB  00:00     

(7/183): cups-libs-1.6.3-26.el7.x86_64.rpm                  | 356 kB  00:00     

(8/183): dbus-libs-1.6.12-17.el7.x86_64.rpm                 | 151 kB  00:00     

(9/183): dbus-1.6.12-17.el7.x86_64.rpm                      | 307 kB  00:00     

(10/183): device-mapper-libs-1.02.135-1.el7_3.4.x86_64.rpm  | 333 kB  00:00     

(11/183): device-mapper-1.02.135-1.el7_3.4.x86_64.rpm       | 269 kB  00:00     

(12/183): dracut-033-463.el7_3.1.x86_64.rpm                 | 317 kB  00:00     

(13/183): fontconfig-2.10.95-10.el7.x86_64.rpm              | 229 kB  00:00     

(14/183): gap-core-4.8.7-0.12.el7.centos.x86_64.rpm         | 2.7 MB  00:00     

(15/183): gap-devel-4.8.7-0.12.el7.centos.x86_64.rpm        | 527 kB  00:00     

(17/183): freetype-2.4.11-1 8% [=-               ]  0.0 B/s |  15 MB  --:-- ETA 

(16/183): freetype-2.4.11-12.el7.x86_64.rpm                 | 391 kB  00:00     

(17/183): fontpackages-filesystem-1.44-8.el7.noarch.rpm     | 9.9 kB  00:00     

(19/183): gap-online-help- 15% [==-              ] 5.5 MB/s |  27 MB  00:25 ETA 

(18/183): gap-online-help-4.8.7-0.12.el7.centos.noarch.rpm  | 8.7 MB  00:00     

(19/183): gmp-devel-6.0.0-12.el7_1.x86_64.rpm               | 181 kB  00:00     

(20/183): ghostscript-fonts-5.50-32.el7.noarch.rpm          | 324 kB  00:00     

(21/183): hardlink-1.0-19.el7.x86_64.rpm                    |  14 kB  00:00     

(22/183): hicolor-icon-theme-0.12-7.el7.noarch.rpm          |  42 kB  00:00     

(23/183): jbigkit-libs-2.0-11.el7.x86_64.rpm                |  46 kB  00:00     

(25/183): ghostscript-9.07 25% [====             ] 8.4 MB/s |  43 MB  00:14 ETA 

(25/183): ghostscript-9.07 26% [====-            ] 8.2 MB/s |  45 MB  00:15 ETA 

(24/183): gap-libs-4.8.7-0.12.el7.centos.noarch.rpm         |  34 MB  00:01     

(27/183): kmod-20-9.el7.x8 32% [=====            ] 9.6 MB/s |  54 MB  00:11 ETA 

(25/183): kmod-20-9.el7.x86_64.rpm                          | 115 kB  00:00     

(26/183): kmod-libs-20-9.el7.x86_64.rpm                     |  47 kB  00:00     

(27/183): kpartx-0.4.9-99.el7_3.3.x86_64.rpm                |  68 kB  00:00     

(30/183): lcms2-2.6-3.el7. 32% [=====-           ] 9.2 MB/s |  56 MB  00:12 ETA 

(28/183): lcms2-2.6-3.el7.x86_64.rpm                        | 150 kB  00:00     

(29/183): libICE-1.0.9-2.el7.x86_64.rpm                     |  65 kB  00:00     

(30/183): libSM-1.2.2-2.el7.x86_64.rpm                      |  39 kB  00:00     

(33/183): libX11-1.6.3-3.e 33% [=====-           ] 8.7 MB/s |  56 MB  00:12 ETA 

(33/183): libX11-1.6.3-3.e 33% [=====-           ] 8.4 MB/s |  57 MB  00:13 ETA 

(31/183): libX11-1.6.3-3.el7.x86_64.rpm                     | 606 kB  00:00     

(32/183): hwdata-0.252-8.4.el7.x86_64.rpm                   | 2.1 MB  00:01     

(33/183): ghostscript-9.07-20.el7_3.5.x86_64.rpm            | 4.3 MB  00:02     

(34/183): libXau-1.0.8-2.1.el7.x86_64.rpm                   |  29 kB  00:00     

(35/183): libX11-common-1.6.3-3.el7.noarch.rpm              | 162 kB  00:00     

(36/183): libXdamage-1.1.4-4.1.el7.x86_64.rpm               |  20 kB  00:00     

(37/183): libXext-1.3.3-3.el7.x86_64.rpm                    |  39 kB  00:00     

(38/183): libXfixes-5.0.1-2.1.el7.x86_64.rpm                |  18 kB  00:00     

(39/183): libXrender-0.9.8-2.1.el7.x86_64.rpm               |  25 kB  00:00     

(40/183): libXfont-1.5.1-2.el7.x86_64.rpm                   | 150 kB  00:00     

(41/183): libXxf86vm-1.1.3-2.1.el7.x86_64.rpm               |  17 kB  00:00     

(42/183): libXt-1.1.4-6.1.el7.x86_64.rpm                    | 173 kB  00:00     

(43/183): libfontenc-1.1.2-3.el7.x86_64.rpm                 |  30 kB  00:00     

(44/183): libdrm-2.4.67-3.el7.x86_64.rpm                    | 141 kB  00:00     

(45/183): libpciaccess-0.13.4-3.el7_3.x86_64.rpm            |  26 kB  00:00     

(46/183): libjpeg-turbo-1.2.90-5.el7.x86_64.rpm             | 134 kB  00:00     

(47/183): libpng-1.5.13-7.el7_2.x86_64.rpm                  | 213 kB  00:00     

(48/183): libxshmfence-1.2-1.el7.x86_64.rpm                 | 7.2 kB  00:00     

(49/183): libxcb-1.11-4.el7.x86_64.rpm                      | 189 kB  00:00     

(50/183): mesa-libEGL-11.2.2-2.20160614.el7.x86_64.rpm      |  85 kB  00:00     

(51/183): libtiff-4.0.3-27.el7_3.x86_64.rpm                 | 170 kB  00:00     

(52/183): mesa-libgbm-11.2.2-2.20160614.el7.x86_64.rpm      |  42 kB  00:00     

(53/183): openjpeg-libs-1.5.1-16.el7_3.x86_64.rpm           |  86 kB  00:00     

(54/183): mesa-libglapi-11.2.2-2.20160614.el7.x86_64.rpm    |  40 kB  00:00     

(55/183): mesa-libGL-11.2.2-2.20160614.el7.x86_64.rpm       | 162 kB  00:00     

(56/183): pixman-0.34.0-1. 35% [======           ] 6.4 MB/s |  61 MB  00:16 ETA 

(56/183): pixman-0.34.0-1.el7.x86_64.rpm                    | 248 kB  00:00     

(57/183): poppler-0.26.5-16.el7.x86_64.rpm                  | 783 kB  00:00     

(58/183): poppler-data-0.4 36% [======           ] 5.8 MB/s |  62 MB  00:18 ETA 

(58/183): procps-ng-3.3.10-10.el7.x86_64.rpm                | 288 kB  00:00     

(59/183): qrencode-libs-3.4.1-3.el7.x86_64.rpm              |  50 kB  00:00     

(60/183): texlive-algorithms-svn15878.0.1-38.el7.noarch.rpm |  21 kB  00:00     

(61/183): poppler-data-0.4 37% [======           ] 5.6 MB/s |  62 MB  00:19 ETA 

(62/183): systemd-219-30.e 37% [======           ] 5.4 MB/s |  64 MB  00:19 ETA 

(62/183): systemd-219-30.e 39% [======-          ] 5.5 MB/s |  66 MB  00:18 ETA 

(61/183): systemd-219-30.el7_3.9.x86_64.rpm                 | 5.2 MB  00:01     

(62/183): texlive-a4wide-svn20943.0-52.el7.noarch.rpm       |  11 kB  00:01     

(64/183): texlive-amsfonts 41% [======-          ] 5.8 MB/s |  69 MB  00:17 ETA 

(63/183): poppler-data-0.4 41% [=======          ] 5.4 MB/s |  70 MB  00:18 ETA 

(63/183): poppler-data-0.4 41% [=======          ] 5.2 MB/s |  70 MB  00:19 ETA 

(63/183): poppler-data-0.4 41% [=======          ] 4.9 MB/s |  71 MB  00:19 ETA 

(64/183): texlive-amsfonts 42% [=======          ] 4.7 MB/s |  71 MB  00:20 ETA 

(63/183): poppler-data-0.4.6-3.el7.noarch.rpm               | 2.2 MB  00:03     

(64/183): texlive-amsmath-svn29327.2.14-38.el7.noarch.rpm   |  49 kB  00:00     

(65/183): texlive-attachfile-svn21866.v1.5b-38.el7.noarch.r |  21 kB  00:00     

(67/183): texlive-babel-sv 42% [=======          ] 4.4 MB/s |  72 MB  00:21 ETA 

(66/183): texlive-babel-svn24756.3.8m-38.el7.noarch.rpm     | 129 kB  00:00     

(67/183): texlive-babelbib-svn25245.1.31-38.el7.noarch.rpm  |  49 kB  00:00     

(69/183): texlive-base-201 43% [=======          ] 4.2 MB/s |  73 MB  00:22 ETA 

(68/183): texlive-bibtex-bin-svn26509.0-38.20130427_r30134. |  65 kB  00:00     

(69/183): texlive-base-2012-38.20130427_r30134.el7.noarch.r | 325 kB  00:00     

(70/183): texlive-breakurl-svn15878.1.30-38.el7.noarch.rpm  |  20 kB  00:00     

(71/183): texlive-booktabs-svn15878.1.61803-38.el7.noarch.r |  19 kB  00:00     

(72/183): texlive-bibtex-svn26689.0.99d-38.el7.noarch.rpm   |  33 kB  00:00     

(73/183): texlive-caption-svn29026.3.3__2013_02_03_-38.el7. |  51 kB  00:00     

(74/183): texlive-cm-svn29581.0-38.el7.noarch.rpm           | 291 kB  00:00     

(75/183): texlive-carlisle-svn18258.0-38.el7.noarch.rpm     |  29 kB  00:00     

(76/183): texlive-chngcntr-svn17157.1.0a-38.el7.noarch.rpm  |  19 kB  00:00     

(77/183): texlive-colortbl-svn25394.v1.0a-38.el7.noarch.rpm |  20 kB  00:00     

(78/183): texlive-csquotes-svn24393.5.1d-38.el7.noarch.rpm  |  36 kB  00:00     

(81/183): texlive-cm-super 43% [=======          ] 4.2 MB/s |  74 MB  00:22 ETA 

(79/183): texlive-currfile-svn29012.0.7b-38.el7.noarch.rpm  |  21 kB  00:00     

(80/183): texlive-dvips-svn29585.0-38.el7.noarch.rpm        | 217 kB  00:00     

(81/183): texlive-amsfonts-svn29208.3.04-38.el7.noarch.rpm  | 3.6 MB  00:03     

(82/183): texlive-enumitem-svn24146.3.5.2-38.el7.noarch.rpm |  29 kB  00:00     

(83/183): texlive-dvips-bin-svn26509.0-38.20130427_r30134.e | 129 kB  00:00     

(84/183): texlive-eso-pic-svn21515.2.0c-38.el7.noarch.rpm   |  21 kB  00:00     

(85/183): texlive-ec-svn25033.1.0-38.el7.noarch.rpm         | 467 kB  00:00     

(86/183): texlive-etex-pkg-svn15878.2.0-38.el7.noarch.rpm   |  22 kB  00:00     

(87/183): texlive-etoolbox-svn20922.2.1-38.el7.noarch.rpm   |  25 kB  00:00     

(88/183): texlive-fancyvrb-svn18492.2.8-38.el7.noarch.rpm   |  30 kB  00:00     

(89/183): texlive-filecontents-svn24250.1.3-38.el7.noarch.r |  19 kB  00:00     

(90/183): texlive-filehook-svn24280.0.5d-38.el7.noarch.rpm  |  22 kB  00:00     

(91/183): texlive-float-svn15878.1.3d-38.el7.noarch.rpm     |  20 kB  00:00     

(94/183): texlive-fontspec 54% [=========        ] 7.4 MB/s |  92 MB  00:10 ETA 

(92/183): texlive-fontspec-svn29412.v2.3a-38.el7.noarch.rpm |  38 kB  00:00     

(93/183): texlive-footmisc-svn23330.5.5b-38.el7.noarch.rpm  |  23 kB  00:00     

(94/183): texlive-fp-svn15878.0-38.el7.noarch.rpm           |  39 kB  00:00     

(95/183): texlive-geometry-svn19716.5.6-38.el7.noarch.rpm   |  26 kB  00:00     

(96/183): texlive-graphics-svn25405.1.0o-38.el7.noarch.rpm  |  33 kB  00:00     

(97/183): texlive-gsftopk-svn26689.1.19.2-38.el7.noarch.rpm |  24 kB  00:00     

(98/183): texlive-gsftopk-bin-svn26509.0-38.20130427_r30134 |  30 kB  00:00     

(99/183): texlive-hyperref-svn28213.6.83m-38.el7.noarch.rpm | 139 kB  00:00     

(100/183): texlive-hyphen-base-svn29197.0-38.el7.noarch.rpm |  39 kB  00:00     

(101/183): texlive-ifetex-svn24853.1.2-38.el7.noarch.rpm    |  18 kB  00:00     

(102/183): texlive-index-svn24099.4.1beta-38.el7.noarch.rpm |  29 kB  00:00     

(103/183): texlive-ifxetex-svn19685.0.5-38.el7.noarch.rpm   |  18 kB  00:00     

(104/183): texlive-kastrup-svn15878.0-38.el7.noarch.rpm     |  18 kB  00:00     

(105/183): texlive-kpathsea-svn28792.0-38.el7.noarch.rpm    | 140 kB  00:00     

(108/183): texlive-helveti 66% [===========      ]  11 MB/s | 113 MB  00:05 ETA 

(106/183): texlive-cm-super-svn15878.0-38.el7.noarch.rpm    |  62 MB  00:01     

(110/183): texlive-kpathse 81% [=============-   ]  15 MB/s | 138 MB  00:01 ETA 

(107/183): texlive-kpathsea-bin-svn27347.0-38.20130427_r301 |  40 kB  00:00     

(108/183): texlive-kpathsea-lib-2012-38.20130427_r30134.el7 |  78 kB  00:00     

(109/183): texlive-l3packages-svn29361.SVN_4467-38.el7.noar |  36 kB  00:00     

(110/183): texlive-latex-svn27907.0-38.el7.noarch.rpm       | 197 kB  00:00     

(111/183): texlive-helvetic-svn28614.0-38.el7.noarch.rpm    | 614 kB  00:00     

(112/183): texlive-latex-bin-svn26689.0-38.el7.noarch.rpm   |  20 kB  00:00     

(113/183): texlive-latex-bin-bin-svn14050.0-38.20130427_r30 |  17 kB  00:00     

(114/183): texlive-latex-fonts-svn28888.0-38.el7.noarch.rpm |  42 kB  00:00     

(115/183): texlive-latexconfig-svn28991.0-38.el7.noarch.rpm |  26 kB  00:00     

(116/183): texlive-listings-svn15878.1.4-38.el7.noarch.rpm  | 138 kB  00:00     

(117/183): texlive-l3kernel-svn29409.SVN_4469-38.el7.noarch | 107 kB  00:00     

(118/183): texlive-lualatex-math-svn29346.1.2-38.el7.noarch |  21 kB  00:00     

(119/183): texlive-luaotfload-svn26718.1.26-38.el7.noarch.r | 101 kB  00:00     

(120/183): texlive-bera-svn20031.0-38.el7.noarch.rpm        | 347 kB  00:01     

(121/183): texlive-luaotfload-bin-svn18579.0-38.20130427_r3 |  17 kB  00:00     

(122/183): texlive-koma-sc 83% [==============   ]  15 MB/s | 140 MB  00:01 ETA 

(122/183): texlive-luatex-svn26689.0.70.1-38.el7.noarch.rpm |  37 kB  00:00     

(123/183): texlive-lm-svn28119.2.004-38.el7.noarch.rpm      |  13 MB  00:00     

(124/183): texlive-luatex-bin-svn26912.0-38.20130427_r30134 | 1.7 MB  00:00     

(125/183): texlive-luatexbase-svn22560.0.31-38.el7.noarch.r |  27 kB  00:00     

(126/183): texlive-makeindex-svn26689.2.12-38.el7.noarch.rp |  30 kB  00:00     

(127/183): texlive-makeindex-bin-svn26509.0-38.20130427_r30 |  38 kB  00:00     

(128/183): texlive-marginnote-svn25880.v1.1i-38.el7.noarch. |  20 kB  00:00     

(129/183): texlive-memoir-svn21638.3.6j_patch_6.0g-38.el7.n |  97 kB  00:00     

(130/183): texlive-mfware-svn26689.0-38.el7.noarch.rpm      |  31 kB  00:00     

(131/183): texlive-mfware-bin-svn26509.0-38.20130427_r30134 |  89 kB  00:00     

(132/183): texlive-mparhack-svn15878.1.4-38.el7.noarch.rpm  |  20 kB  00:00     

(133/183): texlive-ms-svn24467.0-38.el7.noarch.rpm          |  24 kB  00:00     

(134/183): texlive-multido-svn18302.1.42-38.el7.noarch.rpm  |  21 kB  00:00     

(135/183): texlive-ntgclass-svn15878.0-38.el7.noarch.rpm    |  35 kB  00:00     

(136/183): texlive-oberdiek-svn26725.0-38.el7.noarch.rpm    | 307 kB  00:00     

(137/183): texlive-paralist-svn15878.2.3b-38.el7.noarch.rpm |  21 kB  00:00     

(138/183): texlive-parallel-svn15878.0-38.el7.noarch.rpm    |  21 kB  00:00     

(139/183): texlive-pdftex-svn29585.1.40.11-38.el7.noarch.rp | 140 kB  00:00     

(140/183): texlive-koma-sc 92% [===============- ]  17 MB/s | 156 MB  00:00 ETA 

(140/183): texlive-pdftex-bin-svn27321.0-38.20130427_r30134 | 360 kB  00:00     

(141/183): texlive-pgf-svn22614.2.10-38.el7.noarch.rpm      | 468 kB  00:00     

(142/183): texlive-pslatex-svn16416.0-38.el7.noarch.rpm     |  24 kB  00:00     

(143/183): texlive-psnfss-svn23394.9.2a-38.el7.noarch.rpm   |  45 kB  00:00     

(144/183): texlive-pst-3d-svn17257.1.10-38.el7.noarch.rpm   |  21 kB  00:00     

(145/183): texlive-pst-coil-svn24020.1.06-38.el7.noarch.rpm |  21 kB  00:00     

(146/183): texlive-pst-eps-svn15878.1.0-38.el7.noarch.rpm   |  20 kB  00:00     

(147/183): texlive-pst-fill-svn15878.1.01-38.el7.noarch.rpm |  21 kB  00:00     

(148/183): texlive-pst-grad-svn15878.1.06-38.el7.noarch.rpm |  21 kB  00:00     

(149/183): texlive-pst-math-svn20176.0.61-38.el7.noarch.rpm |  22 kB  00:00     

(150/183): texlive-pst-node-svn27799.1.25-38.el7.noarch.rpm |  40 kB  00:00     

(151/183): texlive-pst-plot-svn28729.1.44-38.el7.noarch.rpm |  36 kB  00:00     

(152/183): texlive-pst-text-svn15878.1.00-38.el7.noarch.rpm |  21 kB  00:00     

(153/183): texlive-pst-tree-svn24142.1.12-38.el7.noarch.rpm |  24 kB  00:00     

(154/183): texlive-pstricks-svn29678.2.39-38.el7.noarch.rpm |  97 kB  00:00     

(155/183): texlive-pstricks-add-svn28750.3.59-38.el7.noarch |  41 kB  00:00     

(156/183): texlive-qstest-svn15878.0-38.el7.noarch.rpm      |  22 kB  00:00     

(157/183): texlive-rsfs-svn15878.0-38.el7.noarch.rpm        |  75 kB  00:00     

(158/183): texlive-sauerj-svn15878.0-38.el7.noarch.rpm      |  23 kB  00:00     

(159/183): texlive-setspace-svn24881.6.7a-38.el7.noarch.rpm |  24 kB  00:00     

(160/183): texlive-showexpl-svn27790.v0.3j-38.el7.noarch.rp |  21 kB  00:00     

(161/183): texlive-soul-svn15878.2.4-38.el7.noarch.rpm      |  23 kB  00:00     

(162/183): texlive-subfig-svn15878.1.3-38.el7.noarch.rpm    |  24 kB  00:00     

(163/183): texlive-symbol-svn28614.0-38.el7.noarch.rpm      |  55 kB  00:00     

(164/183): texlive-tetex-svn29585.3.0-38.el7.noarch.rpm     |  88 kB  00:00     

(165/183): texlive-koma-sc 93% [===============- ]  16 MB/s | 158 MB  00:00 ETA 

(165/183): texlive-tetex-bin-svn27344.0-38.20130427_r30134. |  18 kB  00:00     

(166/183): texlive-texlive.infra-svn28217.0-38.el7.noarch.r | 137 kB  00:00     

(167/183): texlive-texlive.infra-bin-svn22566.0-38.20130427 |  16 kB  00:00     

(168/183): texlive-thumbpdf-svn26689.3.15-38.el7.noarch.rpm |  38 kB  00:00     

(169/183): texlive-thumbpdf-bin-svn6898.0-38.20130427_r3013 |  17 kB  00:00     

(170/183): texlive-times-svn28614.0-38.el7.noarch.rpm       | 388 kB  00:00     

(171/183): texlive-tools-svn26263.0-38.el7.noarch.rpm       |  62 kB  00:00     

(172/183): texlive-tipa-svn29349.1.3-38.el7.noarch.rpm      | 2.8 MB  00:00     

(173/183): texlive-underscore-svn18261.0-38.el7.noarch.rpm  |  22 kB  00:00     

(174/183): texlive-unicode-math-svn29413.0.7d-38.el7.noarch |  61 kB  00:00     

(175/183): texlive-url-svn16864.3.2-38.el7.noarch.rpm       |  26 kB  00:00     

(176/183): texlive-varwidth-svn24104.0.92-38.el7.noarch.rpm |  21 kB  00:00     

(177/183): texlive-xcolor-svn15878.2.11-38.el7.noarch.rpm   |  35 kB  00:00     

(178/183): texlive-xunicode-svn23897.0.981-38.el7.noarch.rp |  44 kB  00:00     

(179/183): texlive-xkeyval-svn27995.2.6a-38.el7.noarch.rpm  |  27 kB  00:00     

(180/183): xorg-x11-font-utils-7.5-20.el7.x86_64.rpm        |  87 kB  00:00     

(181/183): zziplib-0.13.62-5.el7.x86_64.rpm                 |  81 kB  00:00     

(182/183): urw-fonts-2.4-16.el7.noarch.rpm                  | 3.0 MB  00:00     

(183/183): texlive-koma-sc 97% [================-]  17 MB/s | 165 MB  00:00 ETA 

(183/183): texlive-koma-sc 98% [================-]  16 MB/s | 165 MB  00:00 ETA 

(183/183): texlive-koma-sc 98% [================-]  15 MB/s | 166 MB  00:00 ETA 

(183/183): texlive-koma-sc 98% [================-]  14 MB/s | 166 MB  00:00 ETA 

(183/183): texlive-koma-sc 98% [================-]  13 MB/s | 167 MB  00:00 ETA 

(183/183): texlive-koma-sc 98% [================-]  12 MB/s | 167 MB  00:00 ETA 

(183/183): texlive-koma-sc 99% [================-]  11 MB/s | 167 MB  00:00 ETA 

(183/183): texlive-koma-sc 99% [================-]  11 MB/s | 168 MB  00:00 ETA 

(183/183): texlive-koma-sc 99% [================-] 9.9 MB/s | 168 MB  00:00 ETA 

(183/183): texlive-koma-sc 99% [================-] 9.3 MB/s | 168 MB  00:00 ETA 

(183/183): texlive-koma-sc 99% [================-] 8.7 MB/s | 169 MB  00:00 ETA 

(183/183): texlive-koma-script-svn27255.3.11b-38.el7.noarch | 5.1 MB  00:05     
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Installed:
  GAPDoc-latex.noarch 0:1.5.1-0.12.el7.centos                                   
  gap-devel.x86_64 0:4.8.7-0.12.el7.centos                                      

Dependency Installed:
  GAPDoc.noarch 0:1.5.1-0.12.el7.centos                                         
  acl.x86_64 0:2.2.51-12.el7                                                    
  avahi-libs.x86_64 0:0.6.31-17.el7                                             
  cairo.x86_64 0:1.14.2-1.el7                                                   
  cryptsetup-libs.x86_64 0:1.7.2-1.el7                                          
  cups-libs.x86_64 1:1.6.3-26.el7                                               
  dbus.x86_64 1:1.6.12-17.el7                                                   
  dbus-libs.x86_64 1:1.6.12-17.el7                                              
  device-mapper.x86_64 7:1.02.135-1.el7_3.4                                     
  device-mapper-libs.x86_64 7:1.02.135-1.el7_3.4                                
  dracut.x86_64 0:033-463.el7_3.1                                               
  fontconfig.x86_64 0:2.10.95-10.el7                                            
  fontpackages-filesystem.noarch 0:1.44-8.el7                                   
  freetype.x86_64 0:2.4.11-12.el7                                               
  gap-core.x86_64 0:4.8.7-0.12.el7.centos                                       
  gap-libs.noarch 0:4.8.7-0.12.el7.centos                                       
  gap-online-help.noarch 0:4.8.7-0.12.el7.centos                                
  ghostscript.x86_64 0:9.07-20.el7_3.5                                          
  ghostscript-fonts.noarch 0:5.50-32.el7                                        
  gmp-devel.x86_64 1:6.0.0-12.el7_1                                             
  hardlink.x86_64 1:1.0-19.el7                                                  
  hicolor-icon-theme.noarch 0:0.12-7.el7                                        
  hwdata.x86_64 0:0.252-8.4.el7                                                 
  jbigkit-libs.x86_64 0:2.0-11.el7                                              
  kmod.x86_64 0:20-9.el7                                                        
  kmod-libs.x86_64 0:20-9.el7                                                   
  kpartx.x86_64 0:0.4.9-99.el7_3.3                                              
  lcms2.x86_64 0:2.6-3.el7                                                      
  libICE.x86_64 0:1.0.9-2.el7                                                   
  libSM.x86_64 0:1.2.2-2.el7                                                    
  libX11.x86_64 0:1.6.3-3.el7                                                   
  libX11-common.noarch 0:1.6.3-3.el7                                            
  libXau.x86_64 0:1.0.8-2.1.el7                                                 
  libXdamage.x86_64 0:1.1.4-4.1.el7                                             
  libXext.x86_64 0:1.3.3-3.el7                                                  
  libXfixes.x86_64 0:5.0.1-2.1.el7                                              
  libXfont.x86_64 0:1.5.1-2.el7                                                 
  libXrender.x86_64 0:0.9.8-2.1.el7                                             
  libXt.x86_64 0:1.1.4-6.1.el7                                                  
  libXxf86vm.x86_64 0:1.1.3-2.1.el7                                             
  libdrm.x86_64 0:2.4.67-3.el7                                                  
  libfontenc.x86_64 0:1.1.2-3.el7                                               
  libjpeg-turbo.x86_64 0:1.2.90-5.el7                                           
  libpciaccess.x86_64 0:0.13.4-3.el7_3                                          
  libpng.x86_64 2:1.5.13-7.el7_2                                                
  libtiff.x86_64 0:4.0.3-27.el7_3                                               
  libxcb.x86_64 0:1.11-4.el7                                                    
  libxshmfence.x86_64 0:1.2-1.el7                                               
  mesa-libEGL.x86_64 0:11.2.2-2.20160614.el7                                    
  mesa-libGL.x86_64 0:11.2.2-2.20160614.el7                                     
  mesa-libgbm.x86_64 0:11.2.2-2.20160614.el7                                    
  mesa-libglapi.x86_64 0:11.2.2-2.20160614.el7                                  
  openjpeg-libs.x86_64 0:1.5.1-16.el7_3                                         
  pixman.x86_64 0:0.34.0-1.el7                                                  
  poppler.x86_64 0:0.26.5-16.el7                                                
  poppler-data.noarch 0:0.4.6-3.el7                                             
  procps-ng.x86_64 0:3.3.10-10.el7                                              
  qrencode-libs.x86_64 0:3.4.1-3.el7                                            
  systemd.x86_64 0:219-30.el7_3.9                                               
  texlive-a4wide.noarch 0:svn20943.0-52.el7                                     
  texlive-algorithms.noarch 2:svn15878.0.1-38.el7                               
  texlive-amsfonts.noarch 2:svn29208.3.04-38.el7                                
  texlive-amsmath.noarch 2:svn29327.2.14-38.el7                                 
  texlive-attachfile.noarch 2:svn21866.v1.5b-38.el7                             
  texlive-babel.noarch 2:svn24756.3.8m-38.el7                                   
  texlive-babelbib.noarch 2:svn25245.1.31-38.el7                                
  texlive-base.noarch 2:2012-38.20130427_r30134.el7                             
  texlive-bera.noarch 2:svn20031.0-38.el7                                       
  texlive-bibtex.noarch 2:svn26689.0.99d-38.el7                                 
  texlive-bibtex-bin.x86_64 2:svn26509.0-38.20130427_r30134.el7                 
  texlive-booktabs.noarch 2:svn15878.1.61803-38.el7                             
  texlive-breakurl.noarch 2:svn15878.1.30-38.el7                                
  texlive-caption.noarch 2:svn29026.3.3__2013_02_03_-38.el7                     
  texlive-carlisle.noarch 2:svn18258.0-38.el7                                   
  texlive-chngcntr.noarch 2:svn17157.1.0a-38.el7                                
  texlive-cm.noarch 2:svn29581.0-38.el7                                         
  texlive-cm-super.noarch 2:svn15878.0-38.el7                                   
  texlive-colortbl.noarch 2:svn25394.v1.0a-38.el7                               
  texlive-csquotes.noarch 2:svn24393.5.1d-38.el7                                
  texlive-currfile.noarch 2:svn29012.0.7b-38.el7                                
  texlive-dvips.noarch 2:svn29585.0-38.el7                                      
  texlive-dvips-bin.x86_64 2:svn26509.0-38.20130427_r30134.el7                  
  texlive-ec.noarch 2:svn25033.1.0-38.el7                                       
  texlive-enumitem.noarch 2:svn24146.3.5.2-38.el7                               
  texlive-eso-pic.noarch 2:svn21515.2.0c-38.el7                                 
  texlive-etex-pkg.noarch 2:svn15878.2.0-38.el7                                 
  texlive-etoolbox.noarch 2:svn20922.2.1-38.el7                                 
  texlive-fancyvrb.noarch 2:svn18492.2.8-38.el7                                 
  texlive-filecontents.noarch 2:svn24250.1.3-38.el7                             
  texlive-filehook.noarch 2:svn24280.0.5d-38.el7                                
  texlive-float.noarch 2:svn15878.1.3d-38.el7                                   
  texlive-fontspec.noarch 2:svn29412.v2.3a-38.el7                               
  texlive-footmisc.noarch 2:svn23330.5.5b-38.el7                                
  texlive-fp.noarch 2:svn15878.0-38.el7                                         
  texlive-geometry.noarch 2:svn19716.5.6-38.el7                                 
  texlive-graphics.noarch 2:svn25405.1.0o-38.el7                                
  texlive-gsftopk.noarch 2:svn26689.1.19.2-38.el7                               
  texlive-gsftopk-bin.x86_64 2:svn26509.0-38.20130427_r30134.el7                
  texlive-helvetic.noarch 2:svn28614.0-38.el7                                   
  texlive-hyperref.noarch 2:svn28213.6.83m-38.el7                               
  texlive-hyphen-base.noarch 2:svn29197.0-38.el7                                
  texlive-ifetex.noarch 2:svn24853.1.2-38.el7                                   
  texlive-ifxetex.noarch 2:svn19685.0.5-38.el7                                  
  texlive-index.noarch 2:svn24099.4.1beta-38.el7                                
  texlive-kastrup.noarch 2:svn15878.0-38.el7                                    
  texlive-koma-script.noarch 2:svn27255.3.11b-38.el7                            
  texlive-kpathsea.noarch 2:svn28792.0-38.el7                                   
  texlive-kpathsea-bin.x86_64 2:svn27347.0-38.20130427_r30134.el7               
  texlive-kpathsea-lib.x86_64 2:2012-38.20130427_r30134.el7                     
  texlive-l3kernel.noarch 2:svn29409.SVN_4469-38.el7                            
  texlive-l3packages.noarch 2:svn29361.SVN_4467-38.el7                          
  texlive-latex.noarch 2:svn27907.0-38.el7                                      
  texlive-latex-bin.noarch 2:svn26689.0-38.el7                                  
  texlive-latex-bin-bin.noarch 2:svn14050.0-38.20130427_r30134.el7              
  texlive-latex-fonts.noarch 2:svn28888.0-38.el7                                
  texlive-latexconfig.noarch 2:svn28991.0-38.el7                                
  texlive-listings.noarch 2:svn15878.1.4-38.el7                                 
  texlive-lm.noarch 2:svn28119.2.004-38.el7                                     
  texlive-lualatex-math.noarch 2:svn29346.1.2-38.el7                            
  texlive-luaotfload.noarch 2:svn26718.1.26-38.el7                              
  texlive-luaotfload-bin.noarch 2:svn18579.0-38.20130427_r30134.el7             
  texlive-luatex.noarch 2:svn26689.0.70.1-38.el7                                
  texlive-luatex-bin.x86_64 2:svn26912.0-38.20130427_r30134.el7                 
  texlive-luatexbase.noarch 2:svn22560.0.31-38.el7                              
  texlive-makeindex.noarch 2:svn26689.2.12-38.el7                               
  texlive-makeindex-bin.x86_64 2:svn26509.0-38.20130427_r30134.el7              
  texlive-marginnote.noarch 2:svn25880.v1.1i-38.el7                             
  texlive-memoir.noarch 2:svn21638.3.6j_patch_6.0g-38.el7                       
  texlive-mfware.noarch 2:svn26689.0-38.el7                                     
  texlive-mfware-bin.x86_64 2:svn26509.0-38.20130427_r30134.el7                 
  texlive-mparhack.noarch 2:svn15878.1.4-38.el7                                 
  texlive-ms.noarch 2:svn24467.0-38.el7                                         
  texlive-multido.noarch 2:svn18302.1.42-38.el7                                 
  texlive-ntgclass.noarch 2:svn15878.0-38.el7                                   
  texlive-oberdiek.noarch 2:svn26725.0-38.el7                                   
  texlive-paralist.noarch 2:svn15878.2.3b-38.el7                                
  texlive-parallel.noarch 2:svn15878.0-38.el7                                   
  texlive-pdftex.noarch 2:svn29585.1.40.11-38.el7                               
  texlive-pdftex-bin.x86_64 2:svn27321.0-38.20130427_r30134.el7                 
  texlive-pgf.noarch 2:svn22614.2.10-38.el7                                     
  texlive-pslatex.noarch 2:svn16416.0-38.el7                                    
  texlive-psnfss.noarch 2:svn23394.9.2a-38.el7                                  
  texlive-pst-3d.noarch 2:svn17257.1.10-38.el7                                  
  texlive-pst-coil.noarch 2:svn24020.1.06-38.el7                                
  texlive-pst-eps.noarch 2:svn15878.1.0-38.el7                                  
  texlive-pst-fill.noarch 2:svn15878.1.01-38.el7                                
  texlive-pst-grad.noarch 2:svn15878.1.06-38.el7                                
  texlive-pst-math.noarch 2:svn20176.0.61-38.el7                                
  texlive-pst-node.noarch 2:svn27799.1.25-38.el7                                
  texlive-pst-plot.noarch 2:svn28729.1.44-38.el7                                
  texlive-pst-text.noarch 2:svn15878.1.00-38.el7                                
  texlive-pst-tree.noarch 2:svn24142.1.12-38.el7                                
  texlive-pstricks.noarch 2:svn29678.2.39-38.el7                                
  texlive-pstricks-add.noarch 2:svn28750.3.59-38.el7                            
  texlive-qstest.noarch 2:svn15878.0-38.el7                                     
  texlive-rsfs.noarch 2:svn15878.0-38.el7                                       
  texlive-sauerj.noarch 2:svn15878.0-38.el7                                     
  texlive-setspace.noarch 2:svn24881.6.7a-38.el7                                
  texlive-showexpl.noarch 2:svn27790.v0.3j-38.el7                               
  texlive-soul.noarch 2:svn15878.2.4-38.el7                                     
  texlive-subfig.noarch 2:svn15878.1.3-38.el7                                   
  texlive-symbol.noarch 2:svn28614.0-38.el7                                     
  texlive-tetex.noarch 2:svn29585.3.0-38.el7                                    
  texlive-tetex-bin.noarch 2:svn27344.0-38.20130427_r30134.el7                  
  texlive-texlive.infra.noarch 2:svn28217.0-38.el7                              
  texlive-texlive.infra-bin.x86_64 2:svn22566.0-38.20130427_r30134.el7          
  texlive-thumbpdf.noarch 2:svn26689.3.15-38.el7                                
  texlive-thumbpdf-bin.noarch 2:svn6898.0-38.20130427_r30134.el7                
  texlive-times.noarch 2:svn28614.0-38.el7                                      
  texlive-tipa.noarch 2:svn29349.1.3-38.el7                                     
  texlive-tools.noarch 2:svn26263.0-38.el7                                      
  texlive-underscore.noarch 2:svn18261.0-38.el7                                 
  texlive-unicode-math.noarch 2:svn29413.0.7d-38.el7                            
  texlive-url.noarch 2:svn16864.3.2-38.el7                                      
  texlive-varwidth.noarch 2:svn24104.0.92-38.el7                                
  texlive-xcolor.noarch 2:svn15878.2.11-38.el7                                  
  texlive-xkeyval.noarch 2:svn27995.2.6a-38.el7                                 
  texlive-xunicode.noarch 2:svn23897.0.981-38.el7                               
  urw-fonts.noarch 0:2.4-16.el7                                                 
  xorg-x11-font-utils.x86_64 1:7.5-20.el7                                       
  zziplib.x86_64 0:0.13.62-5.el7                                                

Complete!
Finish: build setup for gap-pkg-automata-1.13-0.3.el7.centos.src.rpm
Start: rpmbuild gap-pkg-automata-1.13-0.3.el7.centos.src.rpm
Building target platforms: x86_64
Building for target x86_64
Executing(%prep): /bin/sh -e /var/tmp/rpm-tmp.L0cO76
+ umask 022
+ cd /builddir/build/BUILD
+ cd /builddir/build/BUILD
+ rm -rf automata
+ /usr/bin/gzip -dc /builddir/build/SOURCES/automata-1.13.tar.gz
+ /usr/bin/tar -xf -
+ STATUS=0
+ '[' 0 -ne 0 ']'
+ cd automata
+ /usr/bin/chmod -Rf a+rX,u+w,g-w,o-w .
+ echo 'Patch #0 (gap-pkg-automata-viewer.patch):'
Patch #0 (gap-pkg-automata-viewer.patch):
+ /usr/bin/cat /builddir/build/SOURCES/gap-pkg-automata-viewer.patch
+ /usr/bin/patch -p0 --fuzz=0
patching file gap/drawgraph.gd
+ mv PackageInfo.g PackageInfo.g.orig
+ iconv -f ISO8859-1 -t UTF-8 PackageInfo.g.orig
+ fixtimestamp PackageInfo.g
+ touch -r PackageInfo.g.orig PackageInfo.g
+ rm -f PackageInfo.g.orig
+ sed -i.orig 's/\r//' README
+ fixtimestamp README
+ touch -r README.orig README
+ rm -f README.orig
+ rm -f doc/gapdoc.css doc/gapdoc.dtd
+ exit 0
Executing(%build): /bin/sh -e /var/tmp/rpm-tmp.xATv4L
+ umask 022
+ cd /builddir/build/BUILD
+ cd automata
+ ln -s /usr/lib/gap/doc ../../doc
+ mkdir ../pkg
+ ln -s ../automata ../pkg/automata
+ gap -l '/builddir/build/BUILD/automata/..;/usr/lib/gap'
 *********   GAP 4.8.7, 24-Mar-2017, build of 2017-06-14 16:30:42 (UTC)
 *  GAP  *   https://www.gap-system.org
 *********   Architecture: x86_64-redhat-linux-gnu-gcc-default64
 Libs used:  gmp, readline
 Loading the library and packages ...
#I  autpgrp package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  alnuth package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  crisp package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  ctbllib package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  factint package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  fga package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  irredsol package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  laguna package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  polenta package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  polycyclic package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  resclasses package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  sophus package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  tomlib package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
 Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0
 Packages:   GAPDoc 1.5.1
 Try '??help' for help. See also '?copyright', '?cite' and '?authors'
gap> ----------------------------------------------------------------
Loading  Automata 1.13
For help, type: ?Automata: 
----------------------------------------------------------------
true
gap> #I  #I Composing XML document . . .

#I  #I Parsing XML document . . .

#I  #I Checking XML structure . . .

#I  #I Text version (also produces labels for hyperlinks):

#I  #I First run, collecting cross references, index, toc, bib and so on . . .

#I  #I Table of contents complete.

#I  #I Producing the index . . .

#I  #I Reading bibliography data files . . . 

#I  #I   BibTeX format: AutMan

#I  #I   checking and translating to BibXMLext . . .

#I  #I Writing bibliography . . .

#I  #I Second run through document . . .

#I  #I Producing simplified search strings and labels for hyperlinks . . .

#I  #I Constructing LaTeX version and calling pdflatex:

#I  #I Writing LaTeX file, 
#I  3 x pdflatex with bibtex and makeindex, 
#I  
#W WARNING: Something wrong, don't find log file doc/AutMan.log

#I  
#I ERROR: no .pdf file produced (and no .six file)
#I  #I Finally the HTML version . . .

#I  #I First run, collecting cross references, index, toc, bib and so on . . .

#I  #I Table of contents complete.

#I  #I Producing the index . . .

#I  #I Writing bibliography . . .

#I  #I Second run through document . . .

#I  #I - also HTML version for MathJax . . .

#I  #I First run, collecting cross references, index, toc, bib and so on . . .

#I  #I Table of contents complete.

#I  #I Producing the index . . .

#I  #I Writing bibliography . . .

#I  #I Second run through document . . .

rec( Name := "Automata", attributes := rec(  ), bibdata := "AutMan", 
  bibentries := 
    [ <BibXMLext entry: AHU:74>, <BibXMLext entry: KoutsofiosNorth:2002>, 
      <BibXMLext entry: HU:69>, <BibXMLext entry: KM:2002>, 
      <BibXMLext entry: MSW:2001>, <BibXMLext entry: AMORE:95> ], 
  bibkeys := [ "AHU:74", "KoutsofiosNorth:2002", "HU:69", "KM:2002", 
      "MSW:2001", "AMORE:95" ], 
  biblabels := [ "AHU74", "DEGKNW02", "HU69", "KM02", "MSW01", "MMPTV95" ], 
  bibpath := dir("doc/"), bibstrings := [ [ 0, 0 ] ], 
  bibtext := "\n<p><a id=\"biBAHU:74\" name=\"biBAHU:74\"></a></p>\n<p class='\
BibEntry'>\n[<span class='BibKey'>AHU74</span>]   <b class='BibAuthor'>Aho, A.\
 V., Hopcroft, J. E. and Ullman, J. D.</b>,\n <i class='BibTitle'>The Design a\
nd Analisys of Computer Algorithms</i>,\n <span class='BibPublisher'>Addison-W\
esley</span>,\n <span class='BibAddress'>Reading, Mass.</span>\n (<span class=\
'BibYear'>1974</span>).\n</p>\n\n\n<p><a id=\"biBKoutsofiosNorth:2002\" name=\
\"biBKoutsofiosNorth:2002\"></a></p>\n<p class='BibEntry'>\n[<span class='BibK\
ey'>DEGKNW02</span>]   <b class='BibAuthor'>Dobkin, D., Ellson, J., Gansner, E\
., Koutsofios, E., North, S. and Woodhull, G.</b>,\n <i class='BibTitle'>Graph\
viz - Graph Drawing Programs</i>,\n <span class='BibOrganization'>AT\\&amp;T R\
esearch and Lucent Bell Labs</span>\n (<span class='BibYear'>2002</span>)<br /\
>\n(<span class='BibNote'>(http://www.research.att.com/sw/tools/graphviz)</spa\
n>).\n</p>\n\n\n<p><a id=\"biBHU:69\" name=\"biBHU:69\"></a></p>\n<p class='Bi\
bEntry'>\n[<span class='BibKey'>HU69</span>]   <b class='BibAuthor'>Hopcroft, \
J. E. and Ullman, J. D.</b>,\n <i class='BibTitle'>Formal Languages and their \
Relation to Automata</i>,\n <span class='BibPublisher'>Addison-Wesley</span>,\
\n <span class='BibAddress'>Reading, Mass.</span>\n (<span class='BibYear'>196\
9</span>).\n</p>\n\n\n<p><a id=\"biBKM:2002\" name=\"biBKM:2002\"></a></p>\n<p\
 class='BibEntry'>\n[<span class='BibKey'>KM02</span>]   <b class='BibAuthor'>\
Kapovich, I. and Myasnikov, A.</b>,\n <i class='BibTitle'>Stallings foldings a\
nd subgroups of free groups</i>,\n <span class='BibJournal'>J. of Algebra</spa\
n>,\n <em class='BibVolume'>248</em>\n (<span class='BibYear'>2002</span>),\n \
<span class='BibPages'>608--668</span>.\n</p>\n\n\n<p><a id=\"biBMSW:2001\" na\
me=\"biBMSW:2001\"></a></p>\n<p class='BibEntry'>\n[<span class='BibKey'>MSW01\
</span>]   <b class='BibAuthor'>Margolis, S., Sapir, M. and Weil, P.</b>,\n <i\
 class='BibTitle'>Closed subgroups in pro-V topologies and the extension probl\
em\n      for\n  inverse automata</i>,\n <span class='BibJournal'>Int. J. of A\
lgebra and Computation</span>,\n <em class='BibVolume'>11</em>\n (<span class=\
'BibYear'>2001</span>),\n <span class='BibPages'>405--445</span>.\n</p>\n\n\n<\
p><a id=\"biBAMORE:95\" name=\"biBAMORE:95\"></a></p>\n<p class='BibEntry'>\n[\
<span class='BibKey'>MMPTV95</span>]   <b class='BibAuthor'>Matz, O., Miller, \
A., Potthoff, A., Thomas, W. and Valkema, E.</b>,\n <i class='BibTitle'>Report\
 on the program AMoRe</i>,\n <span class='BibOrganization'>Christian Albrechts\
 Universit{\\\"a}t, Kiel</span> (<span class='BibNumber'>9507</span>)\n (<span\
 class='BibYear'>1995</span>).\n</p>\n\n", bookname := "Automata", 
  chapsectlinks := 
    rec( 
      1 := "<div class=\"ChapSects\"><a href=\"chap1_mj.html#X7DFB63A97E67C0A1\
\">1 <span class=\"Heading\">\n      Introduction\n    </span></a>\n</div>\n",
      2 := "<div class=\"ChapSects\"><a href=\"chap2_mj.html#X811E5FC2849C5644\
\">2 <span class=\"Heading\">Finite Automata</span></a>\n<div class=\"ContSect\
\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap2_\
mj.html#X821C3B3687B1F2FF\">2.1 <span class=\"Heading\">Automata generation</s\
pan></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X87D8222D7B507\
31E\">2.1-1 Automaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X83CCDEF9814F1E6D\">2.1-2 Is\
Automaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chap2_mj.html#X7D39CECC7E12DD8A\">2.1-3 IsDeterministi\
cAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap2_mj.html#X83C1148481BAA3DD\">2.1-4 IsNonDetermin\
isticAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X81EC5331790D6022\">2.1-5 IsEpsilon\
Automaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chap2_mj.html#X81FB5BE27903EC32\">2.1-6 String</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap2_mj.html#X801019097C93BCCC\">2.1-7 RandomAutomaton</a></span>\n</d\
iv></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\
\">&nbsp;</span><a href=\"chap2_mj.html#X80AB906D86BBC153\">2.2 <span class=\"\
Heading\">Automata internals</span></a>\n</span>\n<div class=\"ContSSBlock\">\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap2_mj.html#X7A34B47778B50FFE\">2.2-1 AlphabetOfAutomaton</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap2_mj.html#X8044B24B82C59BBF\">2.2-2 AlphabetOfAutomatonAsList</a></span>\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap2_mj.html#X872BB42A81E4D0E7\">2.2-3 TransitionMatrixOfAutomaton</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap2_mj.html#X7B5C3CFA83FF80EA\">2.2-4 InitialStatesOfAutomaton</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap2_mj.html#X8408FE8487028B7F\">2.2-5 SetInitialStatesOfAutomaton</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap2_mj.html#X78CDDCC27D085F00\">2.2-6 FinalStatesOfAutomaton</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap2_mj.html#X80689F1480F9D959\">2.2-7 SetFinalStatesOfAutomaton</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap2_mj.html#X7D22AD207A3D5FF4\">2.2-8 NumberStatesOfAutomaton</a\
></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span \
class=\"nocss\">&nbsp;</span><a href=\"chap2_mj.html#X8454E24E7D9FC1C2\">2.3 <\
span class=\"Heading\">Comparison of automata</span></a>\n</span>\n</div>\n<di\
v class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</spa\
n><a href=\"chap2_mj.html#X867887A683961C63\">2.4 <span class=\"Heading\">Test\
s involving automata</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2\
_mj.html#X8356E41086482483\">2.4-1 IsDenseAutomaton</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.htm\
l#X8676D8388053F1E7\">2.4-2 IsRecognizedByAutomaton</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.htm\
l#X80CCDD438258CD25\">2.4-3 IsPermutationAutomaton</a></span>\n<span class=\"C\
ontSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html\
#X7B7CA23680888C9C\">2.4-4 IsInverseAutomaton</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7A4\
CDEFB84B97849\">2.4-5 AddInverseEdgesToInverseAutomaton</a></span>\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj\
.html#X8321BCE57E55FB30\">2.4-6 IsReversibleAutomaton</a></span>\n</div></div>\
\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;\
</span><a href=\"chap2_mj.html#X82EB5BE77F9F686A\">2.5 <span class=\"Heading\"\
>Basic operations</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj\
.html#X8225A1B886131707\">2.5-1 CopyAutomaton</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X80D\
423A584246E2E\">2.5-2 NullCompletionAutomaton</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X79F\
052EC81135807\">2.5-3 ListSinkStatesAut</a></span>\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X8240136E7\
A26B1A6\">2.5-4 RemovedSinkStates</a></span>\n<span class=\"ContSS\"><br /><sp\
an class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7C0526217BFE7A6\
5\">2.5-5 ReversedAutomaton</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7A4A066583C71ABE\">2.\
5-6 PermutedAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7A72DDF0782E8D5E\">2.5-7 Li\
stPermutedAutomata</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7FA7DF6D87D63D67\">2.5-8 Norma\
lizedAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7A94A77A7C65BA90\">2.5-9 UnionAuto\
mata</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap2_mj.html#X83E772F2878546A4\">2.5-10 ProductAutomaton</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap2_mj.html#X85F6AD697DCA5765\">2.5-11 ProductOfLanguages</a></\
span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span cla\
ss=\"nocss\">&nbsp;</span><a href=\"chap2_mj.html#X79F21CB37B34A354\">2.6 <spa\
n class=\"Heading\">Links with Semigroups</span></a>\n</span>\n<div class=\"Co\
ntSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap2_mj.html#X7B9994827CF94CC7\">2.6-1 TransitionSemigroup</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap2_mj.html#X7E3F29DF86A26347\">2.6-2 SyntacticSemigroupAut</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap2_mj.html#X7D058F0D83D7B49B\">2.6-3 SyntacticSemigroupLang</a></\
span>\n</div></div>\n</div>\n", 
      3 := "<div class=\"ChapSects\"><a href=\"chap3_mj.html#X833D315483172905\
\">3 <span class=\"Heading\">Rational languages</span></a>\n<div class=\"ContS\
ect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"cha\
p3_mj.html#X7C144D368043DE01\">3.1 <span class=\"Heading\">Rational Expression\
s</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X801EC6F38\
568426D\">3.1-1 RationalExpression</a></span>\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7EE5A70F7F237C\
41\">3.1-2 RatExpOnnLetters</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7DA59CBE8571796C\">3.\
1-3 RandomRatExp</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7E3AA84784019E6C\">3.1-4 SizeRa\
tExp</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap3_mj.html#X7DDB46817D6E79BE\">3.1-5 IsRationalExpressio\
n</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap3_mj.html#X8773359880149A98\">3.1-6 AlphabetOfRatExp</a></\
span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><\
a href=\"chap3_mj.html#X84B9922B7C006158\">3.1-7 AlphabetOfRatExpAsList</a></s\
pan>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a\
 href=\"chap3_mj.html#X786A096681CAC3CD\">3.1-8 CopyRatExp</a></span>\n</div><\
/div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&\
nbsp;</span><a href=\"chap3_mj.html#X7FB9270D7E8FABF3\">3.2 <span class=\"Head\
ing\">Comparison of rational expressions</span></a>\n</span>\n</div>\n<div cla\
ss=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a \
href=\"chap3_mj.html#X83A280D47DB3A033\">3.3 <span class=\"Heading\">Operation\
s with rational languages</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap3_mj.html#X8206BD4E82A81D8F\">3.3-1 UnionRatExp</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.htm\
l#X7E29107587611CE2\">3.3-2 ProductRatExp</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X83D8DAE\
6862C8A96\">3.3-3  StarRatExp</a></span>\n</div></div>\n</div>\n", 
      4 := "<div class=\"ChapSects\"><a href=\"chap4_mj.html#X814B7AD47E8EDAFA\
\">4 <span class=\"Heading\">Automata <em>versus</em> rational expressions</sp\
an></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\"\
>&nbsp;</span><a href=\"chap4_mj.html#X7E631B92873300C1\">4.1 <span class=\"He\
ading\">From automata to rational expressions</span></a>\n</span>\n<div class=\
\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap4_mj.html#X8751E3927CA4DEA1\">4.1-1 AutomatonToRatExp \
</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><sp\
an class=\"nocss\">&nbsp;</span><a href=\"chap4_mj.html#X8138227D7E65FC8C\">4.\
2 <span class=\"Heading\">From rational expression to automata</span></a>\n</s\
pan>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X840EEB7B7DD8B03D\">4.2-1 R\
atExpToNDAut</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap4_mj.html#X866BCCB2788E8561\">4.2-2 RatExpToAut\
omaton</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\
\"><span class=\"nocss\">&nbsp;</span><a href=\"chap4_mj.html#X85DCEFB88712056\
E\">4.3 <span class=\"Heading\">\n      Some tests on automata\n    </span></a\
>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X84E0143A860889A6\">4\
.3-1 IsEmptyLang</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X86AA1A5F7E1EEAFE\">4.3-2 IsFull\
Lang</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap4_mj.html#X8346D1B17DBF96E7\">4.3-3 AreEqualLang</a></s\
pan>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a\
 href=\"chap4_mj.html#X7FCB176285FA5BBB\">4.3-4 IsContainedLang</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap4_mj.html#X83F1DE067C2D31A5\">4.3-5 AreDisjointLang</a></span>\n</div></di\
v>\n</div>\n", 
      5 := "<div class=\"ChapSects\"><a href=\"chap5_mj.html#X7919AA9384EBC6A5\
\">5 <span class=\"Heading\">Some functions involving automata</span></a>\n<di\
v class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</spa\
n><a href=\"chap5_mj.html#X8050E142796E0CBF\">5.1 <span class=\"Heading\">From\
 one type to another</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5\
_mj.html#X81E06D518428CA3C\">5.1-1 EpsilonToNFA</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X8\
1DC84E17A170270\">5.1-2 EpsilonToNFASet</a></span>\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X871F807D7\
9CE148C\">5.1-3 EpsilonCompactedAut</a></span>\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X83B0473278DC1\
4F3\">5.1-4 ReducedNFA</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X87D0F9F17F2BEB57\">5.1-5 N\
FAtoDFA</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap5_mj.html#X7B61945581FE4AC6\">5.1-6 FuseSymbolsAut</\
a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span\
 class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X862A34E9801BEB25\">5.2 \
<span class=\"Heading\">Minimalization of an automaton</span></a>\n</span>\n<d\
iv class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7B5B5B10868FB525\">5.2-1 UsefulAut\
omaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap5_mj.html#X83C26846866AEE46\">5.2-2 MinimalizedAut</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap5_mj.html#X7F7AE088808A5D00\">5.2-3  MinimalAutomaton</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap5_mj.html#X7F484D5A781BB643\">5.2-4 AccessibleStates</a></span>\n<sp\
an class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"c\
hap5_mj.html#X804A6BC979DA6E61\">5.2-5 AccessibleAutomaton</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5\
_mj.html#X7BAACCAF7E2D213B\">5.2-6 IntersectionLanguage</a></span>\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj\
.html#X8460C44386EE6225\">5.2-7 AutomatonAllPairsPaths</a></span>\n</div></div\
>\n</div>\n", 
      6 := "<div class=\"ChapSects\"><a href=\"chap6_mj.html#X7AF3E5D081126EBD\
\">6 <span class=\"Heading\">Finite regular languages</span></a>\n<div class=\
\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a hre\
f=\"chap6_mj.html#X85643AEB7E7FB39A\">6.1 <span class=\"Heading\">Dealing with\
 finite regular languages</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap6_mj.html#X82971FC2851B7B30\">6.1-1 IsFiniteRegularLanguage</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap6_mj.html#X7E48CD3E78277FF7\">6.1-2 FiniteRegularLanguageToListOfWords</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap6_mj.html#X7F9C5C6F815773E6\">6.1-3 ListOfWordsToAutomaton</a><\
/span>\n</div></div>\n</div>\n", 
      A := "<div class=\"ChapSects\"><a href=\"chapA_mj.html#X82FB3D357E1BE288\
\">A <span class=\"Heading\">Directed graphs</span></a>\n<div class=\"ContSect\
\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_\
mj.html#X82FB3D357E1BE288\">A.1 <span class=\"Heading\">Directed graphs</span>\
</a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.html#X86CF9F66788B2A24\
\">A.1-1 RandomDiGraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.html#X868EE741872B932D\">A.1-2 V\
ertexInDegree</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chapA_mj.html#X84DF2E8E7A7B32C6\">A.1-3 VertexOutD\
egree</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chapA_mj.html#X7FA6FAAE7AA8715D\">A.1-4 AutoVertexDegree</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chapA_mj.html#X7BA5F1DF7DA89DC5\">A.1-5 ReversedGraph</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chapA_mj.html#X7F23780E7A12A79E\">A.1-6 AutoConnectedComponents</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chapA_mj.html#X7D5288C982F92481\">A.1-7 GraphStronglyConnectedComponents</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chapA_mj.html#X859B7C517AFBD198\">A.1-8 UnderlyingMultiGraphOfAut\
omaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chapA_mj.html#X78CF8E507E100C62\">A.1-9 UnderlyingGraphOf\
Automaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chapA_mj.html#X78869D478792B3AD\">A.1-10 DiGraphToRela\
tion</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chapA_mj.html#X7D63604A8413AAAF\">A.1-11 MSccAutomaton</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chapA_mj.html#X7971EE367B6B7F36\">A.1-12 AutoIsAcyclicGraph</a></spa\
n>\n</div></div>\n</div>\n", 
      B := "<div class=\"ChapSects\"><a href=\"chapB_mj.html#X82D249F0793E6561\
\">B <span class=\"Heading\">\n      Drawing automata\n    </span></a>\n<div c\
lass=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><\
a href=\"chapB_mj.html#X7988DBAB78EA0C06\">B.1 <span class=\"Heading\">\n     \
   Installing some external programs\n      </span></a>\n</span>\n</div>\n<div\
 class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span\
><a href=\"chapB_mj.html#X84C97CA079719B11\">B.2 <span class=\"Heading\">\n   \
     Functions to draw automata\n      </span></a>\n</span>\n<div class=\"Cont\
SSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</s\
pan><a href=\"chapB_mj.html#X7BC2FDA77FD0237B\">B.2-1 DrawAutomaton</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chapB_mj.html#X7AEE146D8391CA3D\">B.2-2 DrawAutomata</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapB_m\
j.html#X7D17B77F829F9CCB\">B.2-3 DrawGraph</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapB_mj.html#X7E478F\
DD807853CA\">B.2-4 DrawSCCAutomaton</a></span>\n</div></div>\n<div class=\"Con\
tSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"c\
hapB_mj.html#X7F5419527FFCD1DF\">B.3 <span class=\"Heading\">Drawings output f\
ormats</span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span class=\"tocl\
ine\"><span class=\"nocss\">&nbsp;</span><a href=\"chapB_mj.html#X795DD98D86A1\
A441\">B.4 <span class=\"Heading\">Drawings extra graph attributes</span></a>\
\n</span>\n</div>\n</div>\n", 
      C := "<div class=\"ChapSects\"><a href=\"chapC_mj.html#X7DBBB0537ADC9899\
\">C <span class=\"Heading\">Inverse automata and subgroups of the free group<\
/span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocs\
s\">&nbsp;</span><a href=\"chapC_mj.html#X7DDDA5127A3D170C\">C.1 <span class=\
\"Heading\">From subgroups to inverse automata</span></a>\n</span>\n<div class\
=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chapC_mj.html#X85358D097C314EB5\">C.1-1 GeneratorsToListR\
epresentation</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chapC_mj.html#X80F3E10784590374\">C.1-2 ListToGene\
ratorsRepresentation</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chapC_mj.html#X7EAFF7E879D115C5\">C.1-3 Flo\
werAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chapC_mj.html#X7F729A4E8784D92E\">C.1-4 FoldFlowerA\
utomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chapC_mj.html#X826D581D794F1BFB\">C.1-5 SubgroupGenToIn\
vAut</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"\
><span class=\"nocss\">&nbsp;</span><a href=\"chapC_mj.html#X85F2060A86DBE62B\
\">C.2 <span class=\"Heading\">From inverse automata to subgroups</span></a>\n\
</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapC_mj.html#X81DA149779A167BD\">C.2-\
1 GeodesicTreeOfInverseAutomaton</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapC_mj.html#X7F117C43814F2CDE\
\">C.2-2 InverseAutomatonToGenerators</a></span>\n</div></div>\n</div>\n" ), 
  chapsectlinkstext := 
    rec( 
      1 := "<div class=\"ChapSects\"><a href=\"chap1_mj.html#X7DFB63A97E67C0A1\
\">1 <span class=\"Heading\">\n      Introduction\n    </span></a>\n</div>\n",
      2 := "<div class=\"ChapSects\"><a href=\"chap2_mj.html#X811E5FC2849C5644\
\">2 <span class=\"Heading\">Finite Automata</span></a>\n<div class=\"ContSect\
\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap2_\
mj.html#X821C3B3687B1F2FF\">2.1 <span class=\"Heading\">Automata generation</s\
pan></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X87D8222D7B507\
31E\">2.1-1 Automaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X83CCDEF9814F1E6D\">2.1-2 Is\
Automaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chap2_mj.html#X7D39CECC7E12DD8A\">2.1-3 IsDeterministi\
cAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap2_mj.html#X83C1148481BAA3DD\">2.1-4 IsNonDetermin\
isticAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X81EC5331790D6022\">2.1-5 IsEpsilon\
Automaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chap2_mj.html#X81FB5BE27903EC32\">2.1-6 String</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap2_mj.html#X801019097C93BCCC\">2.1-7 RandomAutomaton</a></span>\n</d\
iv></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\
\">&nbsp;</span><a href=\"chap2_mj.html#X80AB906D86BBC153\">2.2 <span class=\"\
Heading\">Automata internals</span></a>\n</span>\n<div class=\"ContSSBlock\">\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap2_mj.html#X7A34B47778B50FFE\">2.2-1 AlphabetOfAutomaton</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap2_mj.html#X8044B24B82C59BBF\">2.2-2 AlphabetOfAutomatonAsList</a></span>\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap2_mj.html#X872BB42A81E4D0E7\">2.2-3 TransitionMatrixOfAutomaton</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap2_mj.html#X7B5C3CFA83FF80EA\">2.2-4 InitialStatesOfAutomaton</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap2_mj.html#X8408FE8487028B7F\">2.2-5 SetInitialStatesOfAutomaton</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap2_mj.html#X78CDDCC27D085F00\">2.2-6 FinalStatesOfAutomaton</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap2_mj.html#X80689F1480F9D959\">2.2-7 SetFinalStatesOfAutomaton</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap2_mj.html#X7D22AD207A3D5FF4\">2.2-8 NumberStatesOfAutomaton</a\
></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span \
class=\"nocss\">&nbsp;</span><a href=\"chap2_mj.html#X8454E24E7D9FC1C2\">2.3 <\
span class=\"Heading\">Comparison of automata</span></a>\n</span>\n</div>\n<di\
v class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</spa\
n><a href=\"chap2_mj.html#X867887A683961C63\">2.4 <span class=\"Heading\">Test\
s involving automata</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2\
_mj.html#X8356E41086482483\">2.4-1 IsDenseAutomaton</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.htm\
l#X8676D8388053F1E7\">2.4-2 IsRecognizedByAutomaton</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.htm\
l#X80CCDD438258CD25\">2.4-3 IsPermutationAutomaton</a></span>\n<span class=\"C\
ontSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html\
#X7B7CA23680888C9C\">2.4-4 IsInverseAutomaton</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7A4\
CDEFB84B97849\">2.4-5 AddInverseEdgesToInverseAutomaton</a></span>\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj\
.html#X8321BCE57E55FB30\">2.4-6 IsReversibleAutomaton</a></span>\n</div></div>\
\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;\
</span><a href=\"chap2_mj.html#X82EB5BE77F9F686A\">2.5 <span class=\"Heading\"\
>Basic operations</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj\
.html#X8225A1B886131707\">2.5-1 CopyAutomaton</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X80D\
423A584246E2E\">2.5-2 NullCompletionAutomaton</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X79F\
052EC81135807\">2.5-3 ListSinkStatesAut</a></span>\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X8240136E7\
A26B1A6\">2.5-4 RemovedSinkStates</a></span>\n<span class=\"ContSS\"><br /><sp\
an class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7C0526217BFE7A6\
5\">2.5-5 ReversedAutomaton</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7A4A066583C71ABE\">2.\
5-6 PermutedAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7A72DDF0782E8D5E\">2.5-7 Li\
stPermutedAutomata</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7FA7DF6D87D63D67\">2.5-8 Norma\
lizedAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7A94A77A7C65BA90\">2.5-9 UnionAuto\
mata</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap2_mj.html#X83E772F2878546A4\">2.5-10 ProductAutomaton</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap2_mj.html#X85F6AD697DCA5765\">2.5-11 ProductOfLanguages</a></\
span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span cla\
ss=\"nocss\">&nbsp;</span><a href=\"chap2_mj.html#X79F21CB37B34A354\">2.6 <spa\
n class=\"Heading\">Links with Semigroups</span></a>\n</span>\n<div class=\"Co\
ntSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap2_mj.html#X7B9994827CF94CC7\">2.6-1 TransitionSemigroup</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap2_mj.html#X7E3F29DF86A26347\">2.6-2 SyntacticSemigroupAut</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap2_mj.html#X7D058F0D83D7B49B\">2.6-3 SyntacticSemigroupLang</a></\
span>\n</div></div>\n</div>\n", 
      3 := "<div class=\"ChapSects\"><a href=\"chap3_mj.html#X833D315483172905\
\">3 <span class=\"Heading\">Rational languages</span></a>\n<div class=\"ContS\
ect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"cha\
p3_mj.html#X7C144D368043DE01\">3.1 <span class=\"Heading\">Rational Expression\
s</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X801EC6F38\
568426D\">3.1-1 RationalExpression</a></span>\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7EE5A70F7F237C\
41\">3.1-2 RatExpOnnLetters</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7DA59CBE8571796C\">3.\
1-3 RandomRatExp</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7E3AA84784019E6C\">3.1-4 SizeRa\
tExp</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap3_mj.html#X7DDB46817D6E79BE\">3.1-5 IsRationalExpressio\
n</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap3_mj.html#X8773359880149A98\">3.1-6 AlphabetOfRatExp</a></\
span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><\
a href=\"chap3_mj.html#X84B9922B7C006158\">3.1-7 AlphabetOfRatExpAsList</a></s\
pan>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a\
 href=\"chap3_mj.html#X786A096681CAC3CD\">3.1-8 CopyRatExp</a></span>\n</div><\
/div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&\
nbsp;</span><a href=\"chap3_mj.html#X7FB9270D7E8FABF3\">3.2 <span class=\"Head\
ing\">Comparison of rational expressions</span></a>\n</span>\n</div>\n<div cla\
ss=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a \
href=\"chap3_mj.html#X83A280D47DB3A033\">3.3 <span class=\"Heading\">Operation\
s with rational languages</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap3_mj.html#X8206BD4E82A81D8F\">3.3-1 UnionRatExp</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.htm\
l#X7E29107587611CE2\">3.3-2 ProductRatExp</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X83D8DAE\
6862C8A96\">3.3-3  StarRatExp</a></span>\n</div></div>\n</div>\n", 
      4 := "<div class=\"ChapSects\"><a href=\"chap4_mj.html#X814B7AD47E8EDAFA\
\">4 <span class=\"Heading\">Automata <em>versus</em> rational expressions</sp\
an></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\"\
>&nbsp;</span><a href=\"chap4_mj.html#X7E631B92873300C1\">4.1 <span class=\"He\
ading\">From automata to rational expressions</span></a>\n</span>\n<div class=\
\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap4_mj.html#X8751E3927CA4DEA1\">4.1-1 AutomatonToRatExp \
</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><sp\
an class=\"nocss\">&nbsp;</span><a href=\"chap4_mj.html#X8138227D7E65FC8C\">4.\
2 <span class=\"Heading\">From rational expression to automata</span></a>\n</s\
pan>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X840EEB7B7DD8B03D\">4.2-1 R\
atExpToNDAut</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap4_mj.html#X866BCCB2788E8561\">4.2-2 RatExpToAut\
omaton</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\
\"><span class=\"nocss\">&nbsp;</span><a href=\"chap4_mj.html#X85DCEFB88712056\
E\">4.3 <span class=\"Heading\">\n      Some tests on automata\n    </span></a\
>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X84E0143A860889A6\">4\
.3-1 IsEmptyLang</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X86AA1A5F7E1EEAFE\">4.3-2 IsFull\
Lang</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap4_mj.html#X8346D1B17DBF96E7\">4.3-3 AreEqualLang</a></s\
pan>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a\
 href=\"chap4_mj.html#X7FCB176285FA5BBB\">4.3-4 IsContainedLang</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap4_mj.html#X83F1DE067C2D31A5\">4.3-5 AreDisjointLang</a></span>\n</div></di\
v>\n</div>\n", 
      5 := "<div class=\"ChapSects\"><a href=\"chap5_mj.html#X7919AA9384EBC6A5\
\">5 <span class=\"Heading\">Some functions involving automata</span></a>\n<di\
v class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</spa\
n><a href=\"chap5_mj.html#X8050E142796E0CBF\">5.1 <span class=\"Heading\">From\
 one type to another</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5\
_mj.html#X81E06D518428CA3C\">5.1-1 EpsilonToNFA</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X8\
1DC84E17A170270\">5.1-2 EpsilonToNFASet</a></span>\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X871F807D7\
9CE148C\">5.1-3 EpsilonCompactedAut</a></span>\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X83B0473278DC1\
4F3\">5.1-4 ReducedNFA</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X87D0F9F17F2BEB57\">5.1-5 N\
FAtoDFA</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap5_mj.html#X7B61945581FE4AC6\">5.1-6 FuseSymbolsAut</\
a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span\
 class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X862A34E9801BEB25\">5.2 \
<span class=\"Heading\">Minimalization of an automaton</span></a>\n</span>\n<d\
iv class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7B5B5B10868FB525\">5.2-1 UsefulAut\
omaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap5_mj.html#X83C26846866AEE46\">5.2-2 MinimalizedAut</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap5_mj.html#X7F7AE088808A5D00\">5.2-3  MinimalAutomaton</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap5_mj.html#X7F484D5A781BB643\">5.2-4 AccessibleStates</a></span>\n<sp\
an class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"c\
hap5_mj.html#X804A6BC979DA6E61\">5.2-5 AccessibleAutomaton</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5\
_mj.html#X7BAACCAF7E2D213B\">5.2-6 IntersectionLanguage</a></span>\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj\
.html#X8460C44386EE6225\">5.2-7 AutomatonAllPairsPaths</a></span>\n</div></div\
>\n</div>\n", 
      6 := "<div class=\"ChapSects\"><a href=\"chap6_mj.html#X7AF3E5D081126EBD\
\">6 <span class=\"Heading\">Finite regular languages</span></a>\n<div class=\
\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a hre\
f=\"chap6_mj.html#X85643AEB7E7FB39A\">6.1 <span class=\"Heading\">Dealing with\
 finite regular languages</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap6_mj.html#X82971FC2851B7B30\">6.1-1 IsFiniteRegularLanguage</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap6_mj.html#X7E48CD3E78277FF7\">6.1-2 FiniteRegularLanguageToListOfWords</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap6_mj.html#X7F9C5C6F815773E6\">6.1-3 ListOfWordsToAutomaton</a><\
/span>\n</div></div>\n</div>\n", 
      A := "<div class=\"ChapSects\"><a href=\"chapA_mj.html#X82FB3D357E1BE288\
\">A <span class=\"Heading\">Directed graphs</span></a>\n<div class=\"ContSect\
\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_\
mj.html#X82FB3D357E1BE288\">A.1 <span class=\"Heading\">Directed graphs</span>\
</a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.html#X86CF9F66788B2A24\
\">A.1-1 RandomDiGraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.html#X868EE741872B932D\">A.1-2 V\
ertexInDegree</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chapA_mj.html#X84DF2E8E7A7B32C6\">A.1-3 VertexOutD\
egree</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chapA_mj.html#X7FA6FAAE7AA8715D\">A.1-4 AutoVertexDegree</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chapA_mj.html#X7BA5F1DF7DA89DC5\">A.1-5 ReversedGraph</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chapA_mj.html#X7F23780E7A12A79E\">A.1-6 AutoConnectedComponents</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chapA_mj.html#X7D5288C982F92481\">A.1-7 GraphStronglyConnectedComponents</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chapA_mj.html#X859B7C517AFBD198\">A.1-8 UnderlyingMultiGraphOfAut\
omaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chapA_mj.html#X78CF8E507E100C62\">A.1-9 UnderlyingGraphOf\
Automaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chapA_mj.html#X78869D478792B3AD\">A.1-10 DiGraphToRela\
tion</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chapA_mj.html#X7D63604A8413AAAF\">A.1-11 MSccAutomaton</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chapA_mj.html#X7971EE367B6B7F36\">A.1-12 AutoIsAcyclicGraph</a></spa\
n>\n</div></div>\n</div>\n", 
      B := "<div class=\"ChapSects\"><a href=\"chapB_mj.html#X82D249F0793E6561\
\">B <span class=\"Heading\">\n      Drawing automata\n    </span></a>\n<div c\
lass=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><\
a href=\"chapB_mj.html#X7988DBAB78EA0C06\">B.1 <span class=\"Heading\">\n     \
   Installing some external programs\n      </span></a>\n</span>\n</div>\n<div\
 class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span\
><a href=\"chapB_mj.html#X84C97CA079719B11\">B.2 <span class=\"Heading\">\n   \
     Functions to draw automata\n      </span></a>\n</span>\n<div class=\"Cont\
SSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</s\
pan><a href=\"chapB_mj.html#X7BC2FDA77FD0237B\">B.2-1 DrawAutomaton</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chapB_mj.html#X7AEE146D8391CA3D\">B.2-2 DrawAutomata</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapB_m\
j.html#X7D17B77F829F9CCB\">B.2-3 DrawGraph</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapB_mj.html#X7E478F\
DD807853CA\">B.2-4 DrawSCCAutomaton</a></span>\n</div></div>\n<div class=\"Con\
tSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"c\
hapB_mj.html#X7F5419527FFCD1DF\">B.3 <span class=\"Heading\">Drawings output f\
ormats</span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span class=\"tocl\
ine\"><span class=\"nocss\">&nbsp;</span><a href=\"chapB_mj.html#X795DD98D86A1\
A441\">B.4 <span class=\"Heading\">Drawings extra graph attributes</span></a>\
\n</span>\n</div>\n</div>\n", 
      C := "<div class=\"ChapSects\"><a href=\"chapC_mj.html#X7DBBB0537ADC9899\
\">C <span class=\"Heading\">Inverse automata and subgroups of the free group<\
/span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocs\
s\">&nbsp;</span><a href=\"chapC_mj.html#X7DDDA5127A3D170C\">C.1 <span class=\
\"Heading\">From subgroups to inverse automata</span></a>\n</span>\n<div class\
=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chapC_mj.html#X85358D097C314EB5\">C.1-1 GeneratorsToListR\
epresentation</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chapC_mj.html#X80F3E10784590374\">C.1-2 ListToGene\
ratorsRepresentation</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chapC_mj.html#X7EAFF7E879D115C5\">C.1-3 Flo\
werAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chapC_mj.html#X7F729A4E8784D92E\">C.1-4 FoldFlowerA\
utomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chapC_mj.html#X826D581D794F1BFB\">C.1-5 SubgroupGenToIn\
vAut</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"\
><span class=\"nocss\">&nbsp;</span><a href=\"chapC_mj.html#X85F2060A86DBE62B\
\">C.2 <span class=\"Heading\">From inverse automata to subgroups</span></a>\n\
</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapC_mj.html#X81DA149779A167BD\">C.2-\
1 GeodesicTreeOfInverseAutomaton</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapC_mj.html#X7F117C43814F2CDE\
\">C.2-2 InverseAutomatonToGenerators</a></span>\n</div></div>\n</div>\n" ), 
  chaptitle := 
    rec( 1 := "<span class=\"Heading\">\n      Introduction\n    </span>", 
      2 := "<span class=\"Heading\">Finite Automata</span>", 
      3 := "<span class=\"Heading\">Rational languages</span>", 
      4 := "<span class=\"Heading\">Automata <em>versus</em> rational expressi\
ons</span>", 
      5 := "<span class=\"Heading\">Some functions involving automata</span>",
      6 := "<span class=\"Heading\">Finite regular languages</span>", 
      A := "<span class=\"Heading\">Directed graphs</span>", 
      B := "<span class=\"Heading\">\n      Drawing automata\n    </span>", 
      C := "<span class=\"Heading\">Inverse automata and subgroups of the free\
 group</span>" ), 
  content := 
    [ 
      rec( content := "xml version=\"1.0\" encoding=\"UTF-8\"", 
          count := [ 0, 0, 0, 1 ], name := "XMLPI", root := ~ ), 
      rec( content := "Book SYSTEM \"gapdoc.dtd\"", count := [ 0, 0, 0, 1 ], 
          name := "XMLDOCTYPE", root := ~ ), 
      rec( content := "LaTeX ExtraPreamble=\"\\usepackage{graphicx}\"", 
          count := [ 0, 0, 0, 1 ], name := "XMLPI", root := ~ ), 
      rec( attributes := rec( Name := "Automata" ), 
          content := 
            [ 
              rec( attributes := rec(  ), 
                  content := 
                    [ 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Automata", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 0, 0, 0, 1 ], name := "Title", 
                          next := 191, root := ~, start := 168, stop := 190 ),
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "( Version \n1.13\n\n\n )\n  ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 0, 0, 0, 1 ], name := "Version", 
                          next := 236, root := ~, start := 194, stop := 235 ),
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := " Manuel Delgado \n    ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "mdelgado@fc.up.pt", 
                                          count := [ 0, 0, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "Email", next := 300, root := ~, 
                                  start := 268, stop := 299 ), 
                              rec( content := "\n    ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "http://www.fc.up.pt/cmup/\
mdelgado", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ) ], 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "Homepage", next := 359, root := ~, 
                                  start := 305, stop := 358 ), 
                              rec( content := "\n  ", count := [ 0, 0, 0, 1 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 0, 0, 0, 1 ], 
                          name := "Author", next := 371, root := ~, 
                          start := 239, stop := 370 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := " Steve Linton\n    ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "sal@cs.st-andrews.ac.uk"
                                            , count := [ 0, 0, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "Email", next := 440, root := ~, 
                                  start := 402, stop := 439 ), 
                              rec( content := "\n    ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "http://www-circa.mcs.st-a\
nd.ac.uk/~sal/", count := [ 0, 0, 0, 1 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "Homepage", next := 505, root := ~, 
                                  start := 445, stop := 504 ), 
                              rec( content := "\n  ", count := [ 0, 0, 0, 1 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 0, 0, 0, 1 ], 
                          name := "Author", next := 517, root := ~, 
                          start := 376, stop := 516 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := " José Joäo Morais \n   ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( 
                                  content := " <Email>josejoao@fc.up.pt</Email\
>", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "XMLCOMMENT", 
                                  root := ~ ), 
                              rec( content := "\n  ", count := [ 0, 0, 0, 1 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 0, 0, 0, 1 ], 
                          name := "Author", next := 604, root := ~, 
                          start := 520, stop := 603 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( 
                                  content := " © 2004 by Manuel Delgado, Steve\
 Linton and José Morais ", count := [ 0, 0, 1, 1 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 0, 0, 1, 2 ], mathmode := "Text",
                                  name := "P", next := 689, root := ~, 
                                  start := 685, stop := 688 ), 
                              rec( 
                                  content := "\n              We adopt the cop\
yright regulations of ", count := [ 0, 0, 1, 2 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
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en the first author was in the\nLIAFA at the University of Paris 7, in a post-\
doc. \nEncouraged by J. E. Pin, he began the implementation in ", 
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                              rec( 
                                  content := "3 of\nan algorithm obtained some\
 time before to answer a question from the realm \nof Finite Semigroups propos\
ed by J. Almeida. It is now part of a separate \npackage: ", 
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                                  name := "P", next := 1204, root := ~, 
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ckage on automata was prepared by the first author \nwho gave it the form of a\
 ", count := [ 0, 0, 2, 2 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                , 
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sion, prepared by the first and third authors, \nmany functions have been adde\
d and the performance of many of the existing \nones has been improved. Furthe\
r important improvements, specially concerning performance,\nhave been achieve\
d when the second author joined the group.\n", count := [ 0, 0, 2, 2 ], 
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age is maintained by the first two authors.\n\nBug reports, suggestions and co\
mments are, of course, welcome. Please use our\nemail addresses to this effect\
.\n\n", count := [ 0, 0, 2, 3 ], mathmode := "Text", name := "PCDATA", 
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                                  content := "\n\nThe first author wishes to ac\
knowledge Cyril Nicaud and Paulo Varandas for \ntheir help in programming some\
 functions of the very first version of this \npackage. He wishes also to ackn\
owledge useful discussions and comments by \nCyril Nicaud, Vítor H. Fernandes\
, Jean-Eric Pin and Jorge Almeida.\n", count := [ 0, 0, 3, 1 ], 
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                                  content := "\nThe first author also acknowle\
dges support of FCT through CMUP \nand the FCT and POCTI Project POCTI/32817/M\
AT/2000 which is funded in\ncooperation with the European Community Fund FEDER\
.\n", count := [ 0, 0, 3, 2 ], mathmode := "Text", name := "PCDATA", 
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financial support of FCT and the POCTI program \nthrough a scholarship given b\
y Centro de Matemática da Universidade do Porto.\n", count := [ 0, 0, 3, 3 ],
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ank Mark Kambites for his contribution in finding bugs and making suggestions \
for the improvement of this package.\n", count := [ 0, 0, 3, 4 ], 
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                                  mathmode := "Text", name := "PCDATA", 
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ally) supported by the FCT project PTDC/MAT/65481/2006 and also by the\n", 
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                                  content := " (CMUP), funded by the European \
Regional Development Fund through the program COMPETE and by the Portuguese Go\
vernment through the FCT - Fundaèäo para a Ciência e a Tecnologia under the\
 project PEst-C/MAT/UI0144/2011.\n", count := [ 0, 0, 3, 9 ], 
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                                  mathmode := "Text", name := "Heading", 
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maton is conveniently described through a diagram like the following\n    ", 
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d{center} \\label{fig:aut1} \\end{figure}\n    ", count := [ 1, 0, 0, 4 ], 
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                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
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deterministic) automaton with\n    ", count := [ 1, 0, 0, 5 ], 
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                                  mathmode := "Text", name := "M", 
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                                          name := "PCDATA", root := ~ ) ], 
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 final state.\n    ", count := [ 1, 0, 0, 5 ], mathmode := "Text", 
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                                  root := ~ ), 
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enting the language of the above automaton. \n    ", count := [ 1, 0, 0, 8 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
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                              rec( 
                                  content := "\nKleene's Theorem states that a\
 language is rational if and only if it is the language of a finite automaton.\
\nBoth directions of Kleene's Theorem can be proved constructively, and these \
algorithms, to go from an automaton to a rational expression and ", 
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                                  name := "PCDATA", root := ~ ), 
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                                          count := [ 1, 0, 0, 9 ], 
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                                  root := ~ ), 
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                                  content := "\nOf course, one has to pay atte\
ntion to the size of the output produced. When producing a deterministic autom\
aton equivalent to a given rational expression one can obtain an optimal solut\
ion (the minimal automaton) using standard algorithms ", 
                                  count := [ 1, 0, 0, 10 ], 
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                                  root := ~ ), 
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                                  mathmode := "Text", name := "Cite", 
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                                  count := [ 1, 0, 0, 10 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
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                              rec( 
                                  content := "\nWhen producing a rational expr\
ession for the language of an automaton, and taking into account some reasonab\
le measure for the size of a rational expression, to determine a minimal one i\
s apparently computationally difficult. We use here some heuristic methods (to\
 be published elsewhere) which in practice lead to very reasonable results.\n \
   ", count := [ 1, 0, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 1, 0, 0, 12 ], 
                                  mathmode := "Text", name := "P", 
                                  next := 5774, root := ~, start := 5769, 
                                  stop := 5773 ), 
                              rec( 
                                  content := "\nThe development of this work h\
as benefited from the existence of AMoRE ", count := [ 1, 0, 0, 12 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Key := "AMORE:95" ), 
                                  content := 0, count := [ 1, 0, 0, 12 ], 
                                  mathmode := "Text", name := "Cite", 
                                  next := 5869, root := ~, start := 5846, 
                                  stop := 5868 ), 
                              rec( content := ", a package written in ", 
                                  count := [ 1, 0, 0, 12 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "C", 
                                          count := [ 1, 0, 0, 12 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 1, 0, 0, 12 ], 
                                  mathmode := "Text", name := "C", 
                                  next := 5900, root := ~, start := 5892, 
                                  stop := 5899 ), 
                              rec( 
                                  content := " to handle Automata, Monoids and\
 Regular Expressions. In fact, its manual has been very useful and some of the\
 algorithms implemented here are those implemented in AMoRE. In this package, \
unlike what happened with AMoRE, we do not have to worry about the monoid part\
 in order to make it useful to semigroup theorists, since monoids are already \
implemented in ", count := [ 1, 0, 0, 12 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "GAP", 
                                          count := [ 1, 0, 0, 12 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 1, 0, 0, 12 ], 
                                  mathmode := "Text", name := "Package", 
                                  next := 23, root := ~, start := 1, 
                                  stop := 22 ), 
                              rec( 
                                  content := " and we may take advantage of th\
is fact. We just need a function to compute the transition semigroup of an aut\
omaton.\n\n     ", count := [ 1, 0, 0, 12 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 1, 0, 0, 13 ], 
                                  mathmode := "Text", name := "P", 
                                  next := 6393, root := ~, start := 6388, 
                                  stop := 6392 ), 
                              rec( content := "\n     ", 
                                  count := [ 1, 0, 0, 13 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 1, 0, 0, 14 ], 
                                  mathmode := "Text", name := "P", 
                                  next := 6404, root := ~, start := 6399, 
                                  stop := 6403 ), 
                              rec( 
                                  content := "\nThe parts of this package that\
 have not so directly to do with automata or rational expressions are put into\
 appendices in this manual. Some words about these appendices follow.\n     ",
                                  count := [ 1, 0, 0, 14 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 1, 0, 0, 15 ], 
                                  mathmode := "Text", name := "P", 
                                  next := 6593, root := ~, start := 6588, 
                                  stop := 6592 ), 
                              rec( 
                                  content := "\nUsing the external program Gra\
phviz ", count := [ 1, 0, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  attributes := 
                                    rec( Key := "KoutsofiosNorth:2002" ), 
                                  content := 0, count := [ 1, 0, 0, 15 ], 
                                  mathmode := "Text", name := "Cite", 
                                  next := 6665, root := ~, start := 6630, 
                                  stop := 6664 ), 
                              rec( 
                                  content := " to graph visualization, one can\
 visualize automata. This very convenient tool presently works easily under LI\
NUX.\n     ", count := [ 1, 0, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 1, 0, 0, 16 ], 
                                  mathmode := "Text", name := "P", 
                                  next := 6790, root := ~, start := 6785, 
                                  stop := 6789 ), 
                              rec( 
                                  content := "\nGiven a finitely generated sub\
group of the free group it is possible to compute a flower automaton and perfo\
rm Stallings foldings over it in order to obtain an inverse automaton correspo\
nding to the given subgroup.\n     ", count := [ 1, 0, 0, 16 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 1, 0, 0, 17 ], 
                                  mathmode := "Text", name := "P", 
                                  next := 7016, root := ~, start := 7011, 
                                  stop := 7015 ), 
                              rec( content := "\n  ", 
                                  count := [ 1, 0, 0, 17 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 1, 0, 0, 1 ], 
                          mathmode := "Text", name := "Chapter", 
                          next := 7029, root := ~, start := 3221, 
                          stop := 7028 ), 
                      rec( content := "\n\n", count := [ 1, 0, 0, 17 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := "xml version=\"1.0\" encoding=\"UTF-8\""
                            , count := [ 1, 0, 0, 17 ], mathmode := "Text", 
                          name := "XMLPI", root := ~ ), 
                      rec( content := "\n", count := [ 1, 0, 0, 17 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := " $Id: automata.xml,v 1.13  Exp $ ", 
                          count := [ 1, 0, 0, 17 ], mathmode := "Text", 
                          name := "XMLCOMMENT", root := ~ ), 
                      rec( content := "\n\n", count := [ 1, 0, 0, 17 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Finite Automata", 
                                          count := [ 2, 0, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 0, 0, 2 ], mathmode := "Text",
                                  name := "Heading", next := 7155, root := ~, 
                                  start := 7121, stop := 7154 ), 
                              rec( 
                                  content := "\n\nThis chapter describes the r\
epresentations used in this package for\nfinite automata and some functions to\
 determine information about them.\n", count := [ 2, 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 2, 0, 0, 4 ], mathmode := "Text",
                                  name := "P", next := 7301, root := ~, 
                                  start := 7297, stop := 7300 ), 
                              rec( 
                                  content := "\n We have to remark that the st\
ates of an automaton are always named\n", count := [ 2, 0, 0, 4 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "1,2,3,\\ldots;", 
                                          count := [ 2, 0, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 0, 0, 4 ], mathmode := "Text",
                                  name := "M", next := 7390, root := ~, 
                                  start := 7370, stop := 7389 ), 
                              rec( 
                                  content := " the alphabet may be given by th\
e user. By default \nit is ", count := [ 2, 0, 0, 4 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "\\{a,b,c,\\ldots\\}", 
                                          count := [ 2, 0, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 0, 0, 4 ], mathmode := "Text",
                                  name := "M", next := 7471, root := ~, 
                                  start := 7448, stop := 7470 ), 
                              rec( content := " (or ", 
                                  count := [ 2, 0, 0, 4 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "\\{a_1,a_2,a_3,\\ldots\\\
}", count := [ 2, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                         ) ], count := [ 2, 0, 0, 4 ], 
                                  mathmode := "Text", name := "M", 
                                  next := 7505, root := ~, start := 7476, 
                                  stop := 7504 ), 
                              rec( 
                                  content := " in the \ncase of alphabets with\
 more than ", count := [ 2, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "26", 
                                          count := [ 2, 0, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 0, 0, 4 ], mathmode := "Text",
                                  name := "M", next := 7556, root := ~, 
                                  start := 7547, stop := 7555 ), 
                              rec( content := " letters). \n", 
                                  count := [ 2, 0, 0, 4 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 2, 0, 0, 5 ], mathmode := "Text",
                                  name := "P", next := 7572, root := ~, 
                                  start := 7568, stop := 7571 ), 
                              rec( 
                                  content := "\nThe transition function of an \
automaton with ", count := [ 2, 0, 0, 5 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "q", 
                                          count := [ 2, 0, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 0, 0, 5 ], mathmode := "Text",
                                  name := "M", next := 7626, root := ~, 
                                  start := 7618, stop := 7625 ), 
                              rec( 
                                  content := " states over an alphabet with  "
                                    , count := [ 2, 0, 0, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := " n", 
                                          count := [ 2, 0, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 0, 0, 5 ], mathmode := "Text",
                                  name := "M", next := 7666, root := ~, 
                                  start := 7657, stop := 7665 ), 
                              rec( 
                                  content := " \nletters is represented by a (\
not necessarily dense) ", count := [ 2, 0, 0, 5 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "n\\times q", 
                                          count := [ 2, 0, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 0, 0, 5 ], mathmode := "Text",
                                  name := "M", next := 7736, root := ~, 
                                  start := 7720, stop := 7735 ), 
                              rec( 
                                  content := " \n matrix. Each row of the matr\
ix describes the action of the corresponding\nletter on the states.\nIn the ca\
se of a ", count := [ 2, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "deterministic automaton"
                                            , count := [ 2, 0, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 0, 0, 5 ], mathmode := "Text",
                                  name := "Emph", next := 7887, root := ~, 
                                  start := 7851, stop := 7886 ), 
                              rec( 
                                  content := " (DFA) the entries of the\n matr\
ix are non-negative integers. \nWhen all entries of the transition table \nare\
 positive integers, the automaton is said to be \n", count := [ 2, 0, 0, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "dense", 
                                          count := [ 2, 0, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 0, 0, 5 ], mathmode := "Text",
                                  name := "Emph", next := 8061, root := ~, 
                                  start := 8043, stop := 8060 ), 
                              rec( content := " or ", count := [ 2, 0, 0, 5 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "complete", 
                                          count := [ 2, 0, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 0, 0, 5 ], mathmode := "Text",
                                  name := "Emph", next := 8086, root := ~, 
                                  start := 8065, stop := 8085 ), 
                              rec( content := ".\n", count := [ 2, 0, 0, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  content := "<Index>automaton!complete</Index\
><Index>automaton!dense</Index>", count := [ 2, 0, 0, 5 ], mathmode := "Text",
                                  name := "XMLCOMMENT", root := ~ ), 
                              rec( content := "\n\nIn the case of a ", 
                                  count := [ 2, 0, 0, 5 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "non deterministic automat\
on", count := [ 2, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                         ) ], count := [ 2, 0, 0, 5 ], 
                                  mathmode := "Text", name := "Emph", 
                                  next := 8217, root := ~, start := 8177, 
                                  stop := 8216 ), 
                              rec( 
                                  content := " (NFA) the entries of the\n matr\
ix may be lists of non-negative integers. \n\n", count := [ 2, 0, 0, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Automata with ", 
                                          count := [ 2, 0, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "\\epsilon", 
                                                  count := [ 2, 0, 0, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 0, 0, 5 ],
                                          mathmode := "Text", name := "M", 
                                          next := 8327, root := ~, 
                                          start := 8312, stop := 8326 ), 
                                      rec( content := "-transitions", 
                                          count := [ 2, 0, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 0, 0, 5 ], mathmode := "Text",
                                  name := "Emph", next := 8346, root := ~, 
                                  start := 8292, stop := 8345 ), 
                              rec( 
                                  content := " are also allowed: the \nlast le\
tter of the alphabet is assumed to be  ", count := [ 2, 0, 0, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "\\epsilon", 
                                          count := [ 2, 0, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 0, 0, 5 ], mathmode := "Text",
                                  name := "M", next := 8431, root := ~, 
                                  start := 8416, stop := 8430 ), 
                              rec( content := " and is represented by @.\n\n",
                                  count := [ 2, 0, 0, 5 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Automata generati\
on", count := [ 2, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 1, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 8505, 
                                          root := ~, start := 8467, 
                                          stop := 8504 ), 
                                      rec( content := "  \n", 
                                          count := [ 2, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          content := " In the case of <Emph>no\
n\n deterministic automata</Emph> the entries of the matrix are lists of \nnon\
-negative integers. ", count := [ 2, 1, 0, 3 ], mathmode := "Text", 
                                          name := "XMLCOMMENT", root := ~ ), 
                                      rec( 
                                          content := "\n\nThe way to create an\
 automaton in ", count := [ 2, 1, 0, 3 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "GAP", 
                                                  count := [ 2, 1, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 1, 0, 3 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 23, 
                                          root := ~, start := 1, stop := 22 ),
                                      rec( content := " is the following \n ",
                                          count := [ 2, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "Type, Size, Alph\
abet,TransitionTable, \nInitial, Accepting", Name := "Automaton" ), 
                                                  content := 0, 
                                                  count := [ 2, 1, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 8797, root := ~, 
                                                  start := 8709, stop := 8796 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          content := " The nam\
es chosen for the arguments describe their meaning.", count := [ 2, 1, 1, 3 ],
                                                          mathmode := "Text", 
                                                          name := "XMLCOMMENT"
                                                            , root := ~ ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "T\
ype", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 8890, 
                                                          root := ~, 
                                                          start := 8879, 
                                                          stop := 8889 ), 
                                                      rec( 
                                                          content := " may be \
\n", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
"det\"", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 8911, 
                                                          root := ~, 
                                                          start := 8899, 
                                                          stop := 8910 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
"nondet\"", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 8928, 
                                                          root := ~, 
                                                          start := 8913, 
                                                          stop := 8927 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
"epsilon\"", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 8948, 
                                                          root := ~, 
                                                          start := 8932, 
                                                          stop := 8947 ), 
                                                      rec( 
                                                          content := " accordi\
ng to whether \nthe automaton is deterministic, non deterministic or an automa\
ton with \n", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\epsilon", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 9058, 
                                                          root := ~, 
                                                          start := 9043, 
                                                          stop := 9057 ), 
                                                      rec( 
                                                          content := "-transit\
ions. \n", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
ize", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 9084, 
                                                          root := ~, 
                                                          start := 9073, 
                                                          stop := 9083 ), 
                                                      rec( 
                                                          content := " is a po\
sitive integer representing the\nnumber of states of the automaton. ", 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
lphabet", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 9174, 
                                                          root := ~, 
                                                          start := 9159, 
                                                          stop := 9173 ), 
                                                      rec( 
                                                          content := " is the \
number of\nletters of the alphabet or a list with the letters of the ordered a\
lphabet. \n", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "T\
ransitionTable", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 9291, 
                                                          root := ~, 
                                                          start := 9269, 
                                                          stop := 9290 ), 
                                                      rec( 
                                                          content := " is the \
transition matrix. The\nentries are non-negative integers not greater than the\
 size of the automaton.\nIn the case of non deterministic automata, lists of n\
on-negative integers not \ngreater than the size of the automaton are also all\
owed. ", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
nitial", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 9550, 
                                                          root := ~, 
                                                          start := 9536, 
                                                          stop := 9549 ), 
                                                      rec( 
                                                          content := "\nand ",
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
ccepting", count := [ 2, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 9571, 
                                                          root := ~, 
                                                          start := 9555, 
                                                          stop := 9570 ), 
                                                      rec( 
                                                          content := " are, re\
spectively, the lists of initial and accepting\nstates.  \n", 
                                                          count := 
                                                            [ 2, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
n\ngap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[3,4,0,4]],[1],[4]);\n< determini\
stic automaton on 2 letters with 4 states >\ngap> Display(aut);\n   |  1  2  3\
  4\n-----------------\n a |  3     3  4\n b |  3  4     4\nInitial state:   [\
 1 ]\nAccepting state: [ 4 ]\n\n", count := [ 2, 1, 1, 4 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 9920, 
                                                          root := ~, 
                                                          start := 9636, 
                                                          stop := 9919 ), 
                                                      rec( 
                                                          content := "\nThe al\
phabet of the automaton may be specified:\n", count := [ 2, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> aut:=Automaton(\"det\",4,\"01\",[[3,,3,4],[3,4,0,4]],[1],[4]);\n< determ\
inistic automaton on 2 letters with 4 states >\ngap> Display(aut);\n   |  1  2\
  3  4\n-----------------\n 0 |  3     3  4\n 1 |  3  4     4\nInitial state: \
  [ 1 ]\nAccepting state: [ 4 ]\n", count := [ 2, 1, 1, 6 ], name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 10254, 
                                                          root := ~, 
                                                          start := 9969, 
                                                          stop := 10253 ), 
                                                      rec( 
                                                          content := "\nInstea\
d of leaving a hole in the transition matrix, we may write a ", 
                                                          count := 
                                                            [ 2, 1, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "0\
", count := [ 2, 1, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 10330, 
                                                          root := ~, 
                                                          start := 10322, 
                                                          stop := 10329 ), 
                                                      rec( 
                                                          content := "\n to me\
an that no transition is present. \nNon deterministic automata may be given th\
e same way.\n", count := [ 2, 1, 1, 7 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> ndaut:=Automaton(\"nondet\",4,2,[[3,[1,2],3,0],[3,4,0,[2,3]]],[1],[4]);\
\n< non deterministic automaton on 2 letters with 4 states >\ngap> Display(nda\
ut);\n   |  1       2          3       4\n------------------------------------\
-----\n a | [ 3 ]   [ 1, 2 ]   [ 3 ]\n b | [ 3 ]   [ 4 ]              [ 2, 3 ]\
\nInitial state:   [ 1 ]\nAccepting state: [ 4 ]\n", count := [ 2, 1, 1, 8 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 1, 1, 8 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 10807, 
                                                          root := ~, 
                                                          start := 10426, 
                                                          stop := 10806 ), 
                                                      rec( 
                                                          content := "\nAlso i\
n the same way can be given ", count := [ 2, 1, 1, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\epsilon", count := [ 2, 1, 1, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 10857, 
                                                          root := ~, 
                                                          start := 10842, 
                                                          stop := 10856 ), 
                                                      rec( 
                                                          content := "-automat\
a. The letter ", count := [ 2, 1, 1, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\epsilon", count := [ 2, 1, 1, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 10894, 
                                                          root := ~, 
                                                          start := 10879, 
                                                          stop := 10893 ), 
                                                      rec( 
                                                          content := " is writ\
ten ", count := [ 2, 1, 1, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "@\
", count := [ 2, 1, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 10914, 
                                                          root := ~, 
                                                          start := 10906, 
                                                          stop := 10913 ), 
                                                      rec( 
                                                          content := " instead\
.\n", count := [ 2, 1, 1, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=Automaton(\"epsilon\",3,\"01@\",[[,[2],[3]],[[1,3],,[1]],[[1],[2],\n>\
 [2]]],[2],[2,3]);\n< epsilon automaton on 3 letters with 3 states >\ngap> Dis\
play(x);\n   |  1          2       3\n------------------------------\n 0 |    \
        [ 2 ]   [ 3 ]\n 1 | [ 1, 3 ]           [ 1 ]\n @ | [ 1 ]      [ 2 ]   \
[ 2 ]\nInitial state:    [ 2 ]\nAccepting states: [ 2, 3 ]\n", count := 
                                                                    [ 2, 1, 
                                                                      1, 10 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 1, 1, 10 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 11312, 
                                                          root := ~, 
                                                          start := 10924, 
                                                          stop := 11311 ), 
                                                      rec( 
                                                          content := "\nBigger\
 automata are displayed in another form:\n", count := [ 2, 1, 1, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> aut:=Automaton(\"det\",16,2,[[4,0,0,6,3,1,4,8,7,4,3,0,6,1,6,0],\n> [3,4,\
0,0,6,1,0,6,1,6,1,6,6,4,8,7,4,5]],[1],[4]);\n< deterministic automaton on 2 le\
tters with 16 states >\ngap> Display(aut);\n1    a   4\n1    b   3\n2    b   4\
\n    ... some more lines\n15   a   6\n15   b   8\n16   b   7\nInitial state: \
  [ 1 ]\nAccepting state: [ 4 ]\n", count := [ 2, 1, 1, 12 ], name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 1, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 11721, 
                                                          root := ~, 
                                                          start := 11360, 
                                                          stop := 11720 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 1, 1, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 11736, root := ~, 
                                                  start := 8798, 
                                                  stop := 11735 ) ], 
                                          count := [ 2, 1, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 11750, root := ~, 
                                          start := 8696, stop := 11749 ), 
                                      rec( content := "\n\n", 
                                          count := [ 2, 1, 1, 13 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "O", 
                                                      Name := "IsAutomaton" ),
                                                  content := 0, 
                                                  count := [ 2, 1, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 11799, root := ~, 
                                                  start := 11765, 
                                                  stop := 11798 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nIn the \
presence of an object ", count := [ 2, 1, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
", count := [ 2, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 11851, 
                                                          root := ~, 
                                                          start := 11843, 
                                                          stop := 11850 ), 
                                                      rec( 
                                                          content := ", one ma\
y want to test whether \n", count := [ 2, 1, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
", count := [ 2, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 11891, 
                                                          root := ~, 
                                                          start := 11883, 
                                                          stop := 11890 ), 
                                                      rec( 
                                                          content := " is an a\
utomaton. This may be done using the function ", count := [ 2, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sAutomaton", count := [ 2, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 11963, 
                                                          root := ~, 
                                                          start := 11945, 
                                                          stop := 11962 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=Automaton(\"det\",3,2,[ [ 0, 2, 0 ], [ 0, 1, 0 ] ],[ 3 ],[ 2 ]);;\nga\
p> IsAutomaton(x);\ntrue\n", count := [ 2, 1, 2, 4 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 12095, 
                                                          root := ~, 
                                                          start := 11965, 
                                                          stop := 12094 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 1, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 12110, root := ~, 
                                                  start := 11800, 
                                                  stop := 12109 ) ], 
                                          count := [ 2, 1, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 12124, root := ~, 
                                          start := 11752, stop := 12123 ), 
                                      rec( content := "\n\n", 
                                          count := [ 2, 1, 2, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "IsDeterministic\
Automaton" ), content := 0, count := [ 2, 1, 3, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 12188, root := ~, 
                                                  start := 12139, 
                                                  stop := 12187 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nReturns\
 ", count := [ 2, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 2, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 12222, 
                                                          root := ~, 
                                                          start := 12211, 
                                                          stop := 12221 ), 
                                                      rec( 
                                                          content := " when ",
                                                          count := 
                                                            [ 2, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 12238, 
                                                          root := ~, 
                                                          start := 12228, 
                                                          stop := 12237 ), 
                                                      rec( 
                                                          content := " is a de\
terministic automaton and ", count := [ 2, 1, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 2, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 12284, 
                                                          root := ~, 
                                                          start := 12272, 
                                                          stop := 12283 ), 
                                                      rec( 
                                                          content := " otherwi\
se. \n", count := [ 2, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=Automaton(\"det\",3,2,[ [ 0, 2, 0 ], [ 0, 1, 0 ] ],[ 3 ],[ 2 ]);;\nga\
p> IsDeterministicAutomaton(x);\ntrue\n", count := [ 2, 1, 3, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 1, 3, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 12440, 
                                                          root := ~, 
                                                          start := 12297, 
                                                          stop := 12439 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 12455, root := ~, 
                                                  start := 12189, 
                                                  stop := 12454 ) ], 
                                          count := [ 2, 1, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 12469, root := ~, 
                                          start := 12126, stop := 12468 ), 
                                      rec( content := "\n", 
                                          count := [ 2, 1, 3, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( content := " silentius ", 
                                          count := [ 2, 1, 3, 5 ], 
                                          mathmode := "Text", 
                                          name := "XMLCOMMENT", root := ~ ), 
                                      rec( content := "\n", 
                                          count := [ 2, 1, 3, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "IsNonDeterminis\
ticAutomaton" ), content := 0, count := [ 2, 1, 4, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 12554, root := ~, 
                                                  start := 12502, 
                                                  stop := 12553 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nReturns\
 ", count := [ 2, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 2, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 12588, 
                                                          root := ~, 
                                                          start := 12577, 
                                                          stop := 12587 ), 
                                                      rec( 
                                                          content := " when ",
                                                          count := 
                                                            [ 2, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 12604, 
                                                          root := ~, 
                                                          start := 12594, 
                                                          stop := 12603 ), 
                                                      rec( 
                                                          content := " is a no\
n deterministic automaton and ", count := [ 2, 1, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 2, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 12654, 
                                                          root := ~, 
                                                          start := 12642, 
                                                          stop := 12653 ), 
                                                      rec( 
                                                          content := " otherwi\
se. \n", count := [ 2, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> y:=Automaton(\"nondet\",3,2,[[,[1,3],],[,[2,3],[1,3]]],[1,2],[1,3]);;\ng\
ap> IsNonDeterministicAutomaton(y);\ntrue\n", count := [ 2, 1, 4, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 1, 4, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 12814, 
                                                          root := ~, 
                                                          start := 12667, 
                                                          stop := 12813 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 12829, root := ~, 
                                                  start := 12555, 
                                                  stop := 12828 ) ], 
                                          count := [ 2, 1, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 12843, root := ~, 
                                          start := 12489, stop := 12842 ), 
                                      rec( content := "\n\n", 
                                          count := [ 2, 1, 4, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "IsEpsilonAutoma\
ton" ), content := 0, count := [ 2, 1, 5, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 12901, root := ~, 
                                                  start := 12858, 
                                                  stop := 12900 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nReturns\
 ", count := [ 2, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 2, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 12935, 
                                                          root := ~, 
                                                          start := 12924, 
                                                          stop := 12934 ), 
                                                      rec( 
                                                          content := " when ",
                                                          count := 
                                                            [ 2, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 12951, 
                                                          root := ~, 
                                                          start := 12941, 
                                                          stop := 12950 ), 
                                                      rec( 
                                                          content := " is an "
                                                            , 
                                                          count := 
                                                            [ 2, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\epsilon", count := [ 2, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 12973, 
                                                          root := ~, 
                                                          start := 12958, 
                                                          stop := 12972 ), 
                                                      rec( 
                                                          content := "-automat\
on and ", count := [ 2, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 2, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 13000, 
                                                          root := ~, 
                                                          start := 12988, 
                                                          stop := 12999 ), 
                                                      rec( 
                                                          content := " otherwi\
se. \n", count := [ 2, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> z:=Automaton(\"epsilon\",2,2,[[[1,2],],[[2],[1]]],[1,2],[1,2]);;\ngap> I\
sEpsilonAutomaton(z);\ntrue\n", count := [ 2, 1, 5, 4 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 13146, 
                                                          root := ~, 
                                                          start := 13013, 
                                                          stop := 13145 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 1, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 1, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 13161, root := ~, 
                                                  start := 12902, 
                                                  stop := 13160 ) ], 
                                          count := [ 2, 1, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 13175, root := ~, 
                                          start := 12845, stop := 13174 ), 
                                      rec( content := "\n", 
                                          count := [ 2, 1, 5, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "String" ), 
                                                  content := 0, 
                                                  count := [ 2, 1, 6, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 13220, root := ~, 
                                                  start := 13189, 
                                                  stop := 13219 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\nThe w\
ay  ", count := [ 2, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
AP", count := [ 2, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 23, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 22 ), 
                                                      rec( 
                                                          content := " display\
s an automaton is quite natural, but when one wants to \ndo small changes, for\
 example using ", count := [ 2, 1, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
opy/paste", count := [ 2, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 13367, 
                                                          root := ~, 
                                                          start := 13350, 
                                                          stop := 13366 ), 
                                                      rec( 
                                                          content := ", the us\
e of the function \n", count := [ 2, 1, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
tring", count := [ 2, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 13407, 
                                                          root := ~, 
                                                          start := 13394, 
                                                          stop := 13406 ), 
                                                      rec( 
                                                          content := " (possib\
ly followed by ", count := [ 2, 1, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "P\
rint", count := [ 2, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 13442, 
                                                          root := ~, 
                                                          start := 13430, 
                                                          stop := 13441 ), 
                                                      rec( 
                                                          content := ") may be\
 usefull.\n", count := [ 2, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=Automaton(\"det\",3,2,[ [ 0, 2, 0 ], [ 0, 1, 0 ] ],[ 3 ],[ 2 ]);;\nga\
p> String(x);\n\"Automaton(\\\"det\\\",3,\\\"ab\\\",[ [ 0, 2, 0 ], [ 0, 1, 0 ]\
 ],[ 3 ],[ 2 ]);;\"\ngap> Print(String(x));\nAutomaton(\"det\",3,\"ab\",[ [ 0,\
 2, 0 ], [ 0, 1, 0 ] ],[ 3 ],[ 2 ]);;\n", count := [ 2, 1, 6, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 1, 6, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 13743, 
                                                          root := ~, 
                                                          start := 13460, 
                                                          stop := 13742 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 1, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> z:=Automaton(\"epsilon\",2,2,[[[1,2],],[[2],[1]]],[1,2],[1,2]);;\ngap> P\
rint(String(z));\nAutomaton(\"epsilon\",2,\"a@\",[ [ [ 1, 2 ], [ ] ], [ [ 2 ],\
 [ 1 ] ] ],[ 1, 2 ],[ \\\n1, 2 ]);;\n", count := [ 2, 1, 6, 6 ], name := "PCDA\
TA", root := ~ ) ], count := [ 2, 1, 6, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 13957, 
                                                          root := ~, 
                                                          start := 13744, 
                                                          stop := 13956 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 1, 6, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 1, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 13972, root := ~, 
                                                  start := 13221, 
                                                  stop := 13971 ) ], 
                                          count := [ 2, 1, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 13986, root := ~, 
                                          start := 13176, stop := 13985 ), 
                                      rec( content := "\n\n", 
                                          count := [ 2, 1, 6, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "Type, Size, Alph\
abet", Name := "RandomAutomaton" ), content := 0, count := [ 2, 1, 7, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 14058, root := ~, 
                                                  start := 14001, 
                                                  stop := 14057 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nGiven t\
he ", count := [ 2, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "T\
ype", count := [ 2, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 14094, 
                                                          root := ~, 
                                                          start := 14083, 
                                                          stop := 14093 ), 
                                                      rec( 
                                                          content := ", the ",
                                                          count := 
                                                            [ 2, 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
ize", count := [ 2, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 14111, 
                                                          root := ~, 
                                                          start := 14100, 
                                                          stop := 14110 ), 
                                                      rec( 
                                                          content := " (i.e. t\
he number of states) and the ", count := [ 2, 1, 7, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
lphabet", count := [ 2, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 14163, 
                                                          root := ~, 
                                                          start := 14148, 
                                                          stop := 14162 ), 
                                                      rec( 
                                                          content := " (a posi\
tive integer\nor a list), returns a pseudo random automaton with \nthese param\
eters.\n", count := [ 2, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> RandomAutomaton(\"det\",5,\"ac\");\n< deterministic automaton on 2 lette\
rs with 5 states >\ngap> Display(last);\n   |  1  2  3  4  5\n----------------\
----\n a |     2  3\n c |  2  3\nInitial state:    [ 4 ]\nAccepting states: [ \
3, 4 ]\n\ngap> RandomAutomaton(\"nondet\",3,[\"a\",\"b\",\"c\"]);\n< non deter\
ministic automaton on 3 letters with 3 states >\n\ngap> RandomAutomaton(\"epsi\
lon\",2,\"abc\");\n< epsilon automaton on 4 letters with 2 states >\n\ngap> Ra\
ndomAutomaton(\"epsilon\",2,2);\n< epsilon automaton on 3 letters with 2 state\
s >\ngap> Display(last);\n   |  1          2\n----------------------\n a | [ 1\
, 2 ]\n b | [ 2 ]      [ 1 ]\n @ | [ 1, 2 ]\nInitial state:    [ 2 ]\nAcceptin\
g states: [ 1, 2 ]\n\ngap> a:=RandomTransformation(3);;\ngap> b:=RandomTransfo\
rmation(3);;\ngap> aut:=RandomAutomaton(\"det\",4,[a,b]);\n< deterministic aut\
omaton on 2 letters with 4 states >\n", count := [ 2, 1, 7, 4 ], name := "PCDA\
TA", root := ~ ) ], count := [ 2, 1, 7, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 15129, 
                                                          root := ~, 
                                                          start := 14254, 
                                                          stop := 15128 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 1, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 1, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 15144, root := ~, 
                                                  start := 14059, 
                                                  stop := 15143 ) ], 
                                          count := [ 2, 1, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 15158, root := ~, 
                                          start := 13988, stop := 15157 ), 
                                      rec( content := "\n\n", 
                                          count := [ 2, 1, 7, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 1, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 15170, 
                                  root := ~, start := 8458, stop := 15169 ), 
                              rec( content := "\n\n\n", 
                                  count := [ 2, 1, 7, 5 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Automata internal\
s", count := [ 2, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 2, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 15219, 
                                          root := ~, start := 15182, 
                                          stop := 15218 ), 
                                      rec( 
                                          content := "\nIn this section we des\
cribe the functions used to access the internals of an automaton.\n\n", 
                                          count := [ 2, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "AlphabetOfAutom\
aton" ), content := 0, count := [ 2, 2, 1, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 15367, root := ~, 
                                                  start := 15323, 
                                                  stop := 15366 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\nRetur\
ns the number of symbols in the alphabet of automaton ", count := 
                                                            [ 2, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 15452, 
                                                          root := ~, 
                                                          start := 15442, 
                                                          stop := 15451 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[3,4,0,]],[1],[4]);;\ngap> Alphabet\
OfAutomaton(aut);\n2\n", count := [ 2, 2, 1, 4 ], name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 2, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 15580, 
                                                          root := ~, 
                                                          start := 15454, 
                                                          stop := 15579 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 15595, root := ~, 
                                                  start := 15368, 
                                                  stop := 15594 ) ], 
                                          count := [ 2, 2, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 15609, root := ~, 
                                          start := 15309, stop := 15608 ), 
                                      rec( content := "\n\n\n", 
                                          count := [ 2, 2, 1, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "AlphabetOfAutom\
atonAsList" ), content := 0, count := [ 2, 2, 2, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 15676, root := ~, 
                                                  start := 15626, 
                                                  stop := 15675 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\nRetur\
ns the alphabet of automaton ", count := [ 2, 2, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 15736, 
                                                          root := ~, 
                                                          start := 15726, 
                                                          stop := 15735 ), 
                                                      rec( 
                                                          content := " always\\
nas a list.\n\n Note that when the alphabet of the automaton is given as an in\
teger \n(meaning the number of symbols) \nnot greater than 26 it returns the l\
ist ", count := [ 2, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
"abcd....\"", count := [ 2, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 15916, 
                                                          root := ~, 
                                                          start := 15899, 
                                                          stop := 15915 ), 
                                                      rec( 
                                                          content := ".\nIf th\
e alphabet is given by means of an integer greater than 26, the \nfunction ret\
urns ", count := [ 2, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
 \"a1\", \"a2\", \"a3\", \"a4\", ... ]", count := [ 2, 2, 2, 3 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 16043, 
                                                          root := ~, 
                                                          start := 16005, 
                                                          stop := 16042 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> a:=RandomAutomaton(\"det\",5,\"cat\");\n< deterministic automaton on 3 l\
etters with 5 states >\ngap> AlphabetOfAutomaton(a);\n3\ngap> AlphabetOfAutoma\
tonAsList(a);\n\"cat\"\ngap> a:=RandomAutomaton(\"det\",5,20);\n< deterministi\
c automaton on 20 letters with 5 states >\ngap> AlphabetOfAutomaton(a);\n20\ng\
ap> AlphabetOfAutomatonAsList(a);\n\"abcdefghijklmnopqrst\"\ngap> a:=RandomAut\
omaton(\"det\",5,30);\n< deterministic automaton on 30 letters with 5 states >\
\ngap> AlphabetOfAutomaton(a);\n30\ngap> AlphabetOfAutomatonAsList(a);\n[ \"a1\
\", \"a2\", \"a3\", \"a4\", \"a5\", \"a6\", \"a7\", \"a8\", \"a9\", \"a10\", \
\"a11\", \n  \"a12\", \"a13\", \"a14\", \"a15\", \"a16\", \"a17\", \"a18\", \"\
a19\", \"a20\", \"a21\",\n  \"a22\", \"a23\", \"a24\", \"a25\", \"a26\", \"a27\
\", \"a28\", \"a29\", \"a30\" ]\n", count := [ 2, 2, 2, 4 ], name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 16796, 
                                                          root := ~, 
                                                          start := 16045, 
                                                          stop := 16795 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 16811, root := ~, 
                                                  start := 15677, 
                                                  stop := 16810 ) ], 
                                          count := [ 2, 2, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 16825, root := ~, 
                                          start := 15612, stop := 16824 ), 
                                      rec( content := "\n\n\n\n", 
                                          count := [ 2, 2, 2, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "TransitionMatri\
xOfAutomaton" ), content := 0, count := [ 2, 2, 3, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 16895, root := ~, 
                                                  start := 16843, 
                                                  stop := 16894 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\nRetur\
ns the transition matrix of automaton ", count := [ 2, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 16964, 
                                                          root := ~, 
                                                          start := 16954, 
                                                          stop := 16963 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[3,4,0,]],[1],[4]);;\ngap> Transiti\
onMatrixOfAutomaton(aut);\n[ [ 3, 0, 3, 4 ], [ 3, 4, 0, 0 ] ]\n", count := 
                                                                    [ 2, 2, 
                                                                      3, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 2, 3, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 17133, 
                                                          root := ~, 
                                                          start := 16966, 
                                                          stop := 17132 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 2, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 17148, root := ~, 
                                                  start := 16896, 
                                                  stop := 17147 ) ], 
                                          count := [ 2, 2, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 17162, root := ~, 
                                          start := 16829, stop := 17161 ), 
                                      rec( content := "\n\n\n", 
                                          count := [ 2, 2, 3, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "InitialStatesOf\
Automaton" ), content := 0, count := [ 2, 2, 4, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 17228, root := ~, 
                                                  start := 17179, 
                                                  stop := 17227 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\nRetur\
ns the initial states of automaton ", count := [ 2, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 17294, 
                                                          root := ~, 
                                                          start := 17284, 
                                                          stop := 17293 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[3,4,0,]],[1],[4]);;\ngap> InitialS\
tatesOfAutomaton(aut);\n[ 1 ]\n", count := [ 2, 2, 4, 4 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 17431, 
                                                          root := ~, 
                                                          start := 17296, 
                                                          stop := 17430 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 2, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 17446, root := ~, 
                                                  start := 17229, 
                                                  stop := 17445 ) ], 
                                          count := [ 2, 2, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 17460, root := ~, 
                                          start := 17165, stop := 17459 ), 
                                      rec( content := "\n\n\n", 
                                          count := [ 2, 2, 4, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut, I", 
                                                      Name := "SetInitialState\
sOfAutomaton" ), content := 0, count := [ 2, 2, 5, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 17532, root := ~, 
                                                  start := 17477, 
                                                  stop := 17531 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\nSets \
the initial states of automaton ", count := [ 2, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 17595, 
                                                          root := ~, 
                                                          start := 17585, 
                                                          stop := 17594 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
", count := [ 2, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 17605, 
                                                          root := ~, 
                                                          start := 17597, 
                                                          stop := 17604 ), 
                                                      rec( 
                                                          content := " may be \
a positive integer or a list of positive integers.\n", count := [ 2, 2, 5, 3 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[3,4,0,]],[1],[4]);;\ngap> SetIniti\
alStatesOfAutomaton(aut,4);\ngap> InitialStatesOfAutomaton(aut);\n[ 4 ]\ngap> \
SetInitialStatesOfAutomaton(aut,[2,3]);\ngap> InitialStatesOfAutomaton(aut);\n\
[ 2, 3 ]\n", count := [ 2, 2, 5, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 2, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 17930, 
                                                          root := ~, 
                                                          start := 17664, 
                                                          stop := 17929 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 2, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 17945, root := ~, 
                                                  start := 17533, 
                                                  stop := 17944 ) ], 
                                          count := [ 2, 2, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 17959, root := ~, 
                                          start := 17463, stop := 17958 ), 
                                      rec( content := "\n\n\n", 
                                          count := [ 2, 2, 5, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "FinalStatesOfAu\
tomaton" ), content := 0, count := [ 2, 2, 6, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 18023, root := ~, 
                                                  start := 17976, 
                                                  stop := 18022 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\nRetur\
ns the final states of automaton ", count := [ 2, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 18087, 
                                                          root := ~, 
                                                          start := 18077, 
                                                          stop := 18086 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[3,4,0,]],[1],[4]);;\ngap> FinalSta\
tesOfAutomaton(aut);\n[ 4 ]\n", count := [ 2, 2, 6, 4 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 2, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 18222, 
                                                          root := ~, 
                                                          start := 18089, 
                                                          stop := 18221 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 2, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 2, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 18237, root := ~, 
                                                  start := 18024, 
                                                  stop := 18236 ) ], 
                                          count := [ 2, 2, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 18251, root := ~, 
                                          start := 17962, stop := 18250 ), 
                                      rec( content := "\n\n\n", 
                                          count := [ 2, 2, 6, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut, F", 
                                                      Name := "SetFinalStatesO\
fAutomaton" ), content := 0, count := [ 2, 2, 7, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 18321, root := ~, 
                                                  start := 18268, 
                                                  stop := 18320 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\nSets \
the final states of automaton ", count := [ 2, 2, 7, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 18382, 
                                                          root := ~, 
                                                          start := 18372, 
                                                          stop := 18381 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "F\
", count := [ 2, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 18392, 
                                                          root := ~, 
                                                          start := 18384, 
                                                          stop := 18391 ), 
                                                      rec( 
                                                          content := " may be \
a positive integer or a list of positive integers.\n", count := [ 2, 2, 7, 3 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[3,4,0,]],[1],[4]);;\ngap> FinalSta\
tesOfAutomaton(aut);\n[ 4 ]\ngap> SetFinalStatesOfAutomaton(aut,2);\ngap> Fina\
lStatesOfAutomaton(aut);\n[ 2 ]\n", count := [ 2, 2, 7, 4 ], name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 2, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 18663, 
                                                          root := ~, 
                                                          start := 18451, 
                                                          stop := 18662 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 2, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 2, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 18678, root := ~, 
                                                  start := 18322, 
                                                  stop := 18677 ) ], 
                                          count := [ 2, 2, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 18692, root := ~, 
                                          start := 18254, stop := 18691 ), 
                                      rec( content := "\n\n\n", 
                                          count := [ 2, 2, 7, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "NumberStatesOfA\
utomaton" ), content := 0, count := [ 2, 2, 8, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 18757, root := ~, 
                                                  start := 18709, 
                                                  stop := 18756 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\nRetur\
ns the number of states of automaton ", count := [ 2, 2, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 2, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 2, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 18825, 
                                                          root := ~, 
                                                          start := 18815, 
                                                          stop := 18824 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 2, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[3,4,0,]],[1],[4]);;\ngap> NumberSt\
atesOfAutomaton(aut);\n4\n", count := [ 2, 2, 8, 4 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 2, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 18957, 
                                                          root := ~, 
                                                          start := 18827, 
                                                          stop := 18956 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 2, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 2, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 18972, root := ~, 
                                                  start := 18758, 
                                                  stop := 18971 ) ], 
                                          count := [ 2, 2, 8, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 18986, root := ~, 
                                          start := 18695, stop := 18985 ), 
                                      rec( content := "\n\n", 
                                          count := [ 2, 2, 8, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 2, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 18998, 
                                  root := ~, start := 15173, stop := 18997 ), 
                              rec( content := "\n\n\n\n", 
                                  count := [ 2, 2, 8, 5 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Comparison of aut\
omata", count := [ 2, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 2, 3, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 19052, 
                                          root := ~, start := 19011, 
                                          stop := 19051 ), 
                                      rec( 
                                          content := "\nAlthough there is no s\
tandard way to compare automata it is usefull to be able to do some kind of co\
mparison. Doing so, one can consider sets of automata.\n We just compare the s\
trings of the automata.\n", count := [ 2, 3, 0, 3 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\ngap> x:=Automat\
on(\"det\",3,2,[ [ 0, 2, 0 ], [ 0, 1, 0 ] ],[ 3 ],[ 2 ]);;\ngap> y:=Automaton(\
\"det\",3,2,[ [ 2, 0, 0 ], [ 1, 3, 0 ] ],[ 3 ],[ 2, 3 ]);;\ngap> x=y;\nfalse\n\
gap> Size(Set([y,x,x]));\n2\n", count := [ 2, 3, 0, 4 ], name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 2, 3, 0, 4 ], 
                                          mathmode := "Text", name := "Log", 
                                          next := 19456, root := ~, 
                                          start := 19254, stop := 19455 ), 
                                      rec( content := "\n", 
                                          count := [ 2, 3, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 3, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 19467, 
                                  root := ~, start := 19002, stop := 19466 ), 
                              rec( content := "\n", count := [ 2, 3, 0, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Tests involving a\
utomata", count := [ 2, 4, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 2, 4, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 19520, 
                                          root := ~, start := 19477, 
                                          stop := 19519 ), 
                                      rec( 
                                          content := "\n\nThis section describ\
es some useful tests involving automata.\n\n", count := [ 2, 4, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "IsDenseAutomato\
n" ), content := 0, count := [ 2, 4, 1, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 19639, root := ~, 
                                                  start := 19598, 
                                                  stop := 19638 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\nTests\
 whether a deterministic automaton ", count := [ 2, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 19705, 
                                                          root := ~, 
                                                          start := 19695, 
                                                          stop := 19704 ), 
                                                      rec( 
                                                          content := " is comp\
lete. \n(See also ", count := [ 2, 4, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "NullCom\
pletionAutomaton" ), content := 0, count := [ 2, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 19767, 
                                                          root := ~, 
                                                          start := 19730, 
                                                          stop := 19766 ), 
                                                      rec( 
                                                          content := ".)  \n",
                                                          count := 
                                                            [ 2, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[3,4,0,]],[1],[4]);;\ngap> IsDenseA\
utomaton(aut);                                 \nfalse\n", count := [ 2, 4, 
                                                                      1, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 4, 1, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 19932, 
                                                          root := ~, 
                                                          start := 19772, 
                                                          stop := 19931 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 4, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 19947, root := ~, 
                                                  start := 19640, 
                                                  stop := 19946 ) ], 
                                          count := [ 2, 4, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 19961, root := ~, 
                                          start := 19584, stop := 19960 ), 
                                      rec( content := "\n\n", 
                                          count := [ 2, 4, 1, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A,w", 
                                                      Name := "IsRecognizedByA\
utomaton" ), content := 0, count := [ 2, 4, 2, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 20025, root := ~, 
                                                  start := 19977, 
                                                  stop := 20024 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nThe arg\
uments are: an automaton ", count := [ 2, 4, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 2, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 20080, 
                                                          root := ~, 
                                                          start := 20072, 
                                                          stop := 20079 ), 
                                                      rec( 
                                                          content := " and a s\
tring (i.e. a word) ", count := [ 2, 4, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "w\
", count := [ 2, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 20116, 
                                                          root := ~, 
                                                          start := 20108, 
                                                          stop := 20115 ), 
                                                      rec( 
                                                          content := " in the \
alphabet of the automaton. \nReturns ", count := [ 2, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 2, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 20171, 
                                                          root := ~, 
                                                          start := 20160, 
                                                          stop := 20170 ), 
                                                      rec( 
                                                          content := " if the \
word is recognized by the automaton \n and ", count := [ 2, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 2, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 20233, 
                                                          root := ~, 
                                                          start := 20221, 
                                                          stop := 20232 ), 
                                                      rec( 
                                                          content := " otherwi\
se. \n\n", count := [ 2, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> aut:=Automaton(\"det\",3,2,[[1,2,1],[2,1,3]],[1],[2]);;\ngap> IsRecogniz\
edByAutomaton(aut,\"bbb\");\ntrue\n\ngap> aut:=Automaton(\"det\",3,\"01\",[[1,\
2,1],[2,1,3]],[1],[2]);;\ngap> IsRecognizedByAutomaton(aut,\"111\");\ntrue\n",
                                                                  count := 
                                                                    [ 2, 4, 
                                                                      2, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 4, 2, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 20493, 
                                                          root := ~, 
                                                          start := 20247, 
                                                          stop := 20492 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 4, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 4, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 20508, root := ~, 
                                                  start := 20026, 
                                                  stop := 20507 ) ], 
                                          count := [ 2, 4, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 20522, root := ~, 
                                          start := 19963, stop := 20521 ), 
                                      rec( content := "\n\n\n", 
                                          count := [ 2, 4, 2, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "IsPermutationAu\
tomaton" ), content := 0, count := [ 2, 4, 3, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 20585, root := ~, 
                                                  start := 20538, 
                                                  stop := 20584 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nThe arg\
ument is a deterministic automaton. Returns ", count := [ 2, 4, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 2, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 4, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 20662, 
                                                          root := ~, 
                                                          start := 20651, 
                                                          stop := 20661 ), 
                                                      rec( 
                                                          content := " when ea\
ch letter of the alphabet induces a permutation on the vertices and ", 
                                                          count := 
                                                            [ 2, 4, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 2, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 4, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 20750, 
                                                          root := ~, 
                                                          start := 20738, 
                                                          stop := 20749 ), 
                                                      rec( 
                                                          content := " otherwi\
se. ", count := [ 2, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=Automaton(\"det\",3,2,[ [ 1, 2, 3 ], [ 1, 2, 3 ] ],[ 1 ],[ 2, 3 ]);;\
\ngap> IsPermutationAutomaton(x);\ntrue\n", count := [ 2, 4, 3, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 4, 3, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 20906, 
                                                          root := ~, 
                                                          start := 20762, 
                                                          stop := 20905 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 4, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 4, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 20921, root := ~, 
                                                  start := 20586, 
                                                  stop := 20920 ) ], 
                                          count := [ 2, 4, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 20935, root := ~, 
                                          start := 20525, stop := 20934 ), 
                                      rec( content := "\n\n", 
                                          count := [ 2, 4, 3, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "IsInverseAutoma\
ton" ), content := 0, count := [ 2, 4, 4, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 20993, root := ~, 
                                                  start := 20950, 
                                                  stop := 20992 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nThe arg\
ument is a deterministic automaton. Returns ", count := [ 2, 4, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 2, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 4, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 21070, 
                                                          root := ~, 
                                                          start := 21059, 
                                                          stop := 21069 ), 
                                                      rec( 
                                                          content := " when ea\
ch letter of the alphabet induces an injective partial function on the vertice\
s and ", count := [ 2, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 2, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 4, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 21174, 
                                                          root := ~, 
                                                          start := 21162, 
                                                          stop := 21173 ), 
                                                      rec( 
                                                          content := " otherwi\
se. ", count := [ 2, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=Automaton(\"det\",3,2,[ [ 0, 1, 3 ], [ 0, 1, 2 ] ],[ 2 ],[ 1 ]);;\nga\
p> IsInverseAutomaton(x);\ntrue\n", count := [ 2, 4, 4, 4 ], name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 4, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 21323, 
                                                          root := ~, 
                                                          start := 21186, 
                                                          stop := 21322 ), 
                                                      rec( 
                                                          content := "\n\nFreq\
uently an inverse automaton is thought as if the inverse edges (labeled by for\
mal inverses of the letters of the alphabet) were present, although they are u\
sually not explicited. They can be made explicit using the function ", 
                                                          count := 
                                                            [ 2, 4, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
ddInverseEdgesToInverseAutomaton", count := [ 2, 4, 4, 5 ], mathmode := "Text"
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 4, 4, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 21593, 
                                                          root := ~, 
                                                          start := 21553, 
                                                          stop := 21592 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 4, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 4, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 21608, root := ~, 
                                                  start := 20994, 
                                                  stop := 21607 ) ], 
                                          count := [ 2, 4, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 21622, root := ~, 
                                          start := 20937, stop := 21621 ), 
                                      rec( content := "\n\n", 
                                          count := [ 2, 4, 4, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "AddInverseEdges\
ToInverseAutomaton" ), content := 0, count := [ 2, 4, 5, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 21695, root := ~, 
                                                  start := 21637, 
                                                  stop := 21694 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nThe arg\
ument is an inverse automaton over the alphabet ", count := [ 2, 4, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\{a,b,c,\\ldots\\}", count := [ 2, 4, 5, 3 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 2, 4, 5, 3 ], mathmode := "Text", 
                                                          name := "M", 
                                                          next := 21788, 
                                                          root := ~, 
                                                          start := 21765, 
                                                          stop := 21787 ), 
                                                      rec( 
                                                          content := ". Return\
s an automaton with the inverse edges added. (The formal inverse of a letter i\
s represented by the corresponding capital letter.)\n ", count := 
                                                            [ 2, 4, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=Automaton(\"det\",3,2,[[ 0, 1, 3 ],[ 0, 1, 2 ]],[ 2 ],[ 1 ]);;Display\
(x);\n   |  1  2  3\n--------------\n a |     1  3\n b |     1  2\nInitial sta\
te:   [ 2 ]\nAccepting state: [ 1 ]\ngap> AddInverseEdgesToInverseAutomaton(x)\
;Display(x);\n   |  1  2  3\n--------------\n a |     1  3\n b |     1  2\n A \
|  2     3\n B |  2  3\nInitial state:   [ 2 ]\nAccepting state: [ 1 ]\n", 
                                                                  count := 
                                                                    [ 2, 4, 
                                                                      5, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 4, 5, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 22324, 
                                                          root := ~, 
                                                          start := 21927, 
                                                          stop := 22323 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 4, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 4, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 22339, root := ~, 
                                                  start := 21696, 
                                                  stop := 22338 ) ], 
                                          count := [ 2, 4, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 22353, root := ~, 
                                          start := 21624, stop := 22352 ), 
                                      rec( content := "\n\n", 
                                          count := [ 2, 4, 5, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "IsReversibleAut\
omaton" ), content := 0, count := [ 2, 4, 6, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 22414, root := ~, 
                                                  start := 22368, 
                                                  stop := 22413 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nThe arg\
ument is a deterministic automaton. \nReturns ", count := [ 2, 4, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 2, 4, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 4, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 22492, 
                                                          root := ~, 
                                                          start := 22481, 
                                                          stop := 22491 ), 
                                                      rec( 
                                                          content := " when ",
                                                          count := 
                                                            [ 2, 4, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 4, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 4, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 22508, 
                                                          root := ~, 
                                                          start := 22498, 
                                                          stop := 22507 ), 
                                                      rec( 
                                                          content := " is a re\
versible automaton, i.e. the automaton obtained by reversing all edges and swi\
tching the initial and final states \n(see also ", count := [ 2, 4, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Reverse\
dAutomaton" ), content := 0, count := [ 2, 4, 6, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 22672, 
                                                          root := ~, 
                                                          start := 22641, 
                                                          stop := 22671 ), 
                                                      rec( 
                                                          content := ") is det\
erministic. Returns ", count := [ 2, 4, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 2, 4, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 4, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 22712, 
                                                          root := ~, 
                                                          start := 22700, 
                                                          stop := 22711 ), 
                                                      rec( 
                                                          content := " otherwi\
se.\n", count := [ 2, 4, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=Automaton(\"det\",3,2,[ [ 0, 1, 2 ], [ 0, 1, 3 ] ],[ 2 ],[ 2 ]);;\nga\
p> IsReversibleAutomaton(x);\ntrue\n", count := [ 2, 4, 6, 4 ], name := "PCDAT\
A", root := ~ ) ], count := [ 2, 4, 6, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 22864, 
                                                          root := ~, 
                                                          start := 22724, 
                                                          stop := 22863 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 4, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 4, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 22879, root := ~, 
                                                  start := 22415, 
                                                  stop := 22878 ) ], 
                                          count := [ 2, 4, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 22893, root := ~, 
                                          start := 22355, stop := 22892 ), 
                                      rec( content := "\n\n", 
                                          count := [ 2, 4, 6, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 4, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 22905, 
                                  root := ~, start := 19468, stop := 22904 ), 
                              rec( content := "\n\n", count := [ 2, 4, 6, 5 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Basic operations"
                                                    , count := [ 2, 5, 0, 2 ],
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 5, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 22951, 
                                          root := ~, start := 22916, 
                                          stop := 22950 ), 
                                      rec( content := "\n\n\n", 
                                          count := [ 2, 5, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "CopyAutomaton" 
                                                     ), content := 0, 
                                                  count := [ 2, 5, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 23005, root := ~, 
                                                  start := 22967, 
                                                  stop := 23004 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nReturns\
 a new automaton, which is a copy of automaton ", count := [ 2, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 23084, 
                                                          root := ~, 
                                                          start := 23074, 
                                                          stop := 23083 ), 
                                                      rec( content := ".\n ", 
                                                          count := 
                                                            [ 2, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 23101, root := ~, 
                                                  start := 23006, 
                                                  stop := 23100 ) ], 
                                          count := [ 2, 5, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 23115, root := ~, 
                                          start := 22954, stop := 23114 ), 
                                      rec( content := "  \n\n\n ", 
                                          count := [ 2, 5, 1, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "NullCompletionA\
utomaton" ), content := 0, count := [ 2, 5, 2, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 23183, root := ~, 
                                                  start := 23135, 
                                                  stop := 23182 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n\n", 
                                                          count := 
                                                            [ 2, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 23209, 
                                                          root := ~, 
                                                          start := 23199, 
                                                          stop := 23208 ), 
                                                      rec( 
                                                          content := " is a de\
terministic automaton. If it is complete returns ", count := [ 2, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 23276, 
                                                          root := ~, 
                                                          start := 23266, 
                                                          stop := 23275 ), 
                                                      rec( 
                                                          content := ",\nother\
wise returns the completion (with a null state) of ", count := [ 2, 5, 2, 3 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 23344, 
                                                          root := ~, 
                                                          start := 23334, 
                                                          stop := 23343 ), 
                                                      rec( 
                                                          content := ". Notice\
 that the words recognized by  ", count := [ 2, 5, 2, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 23393, 
                                                          root := ~, 
                                                          start := 23383, 
                                                          stop := 23392 ), 
                                                      rec( 
                                                          content := " and its\
 completion are the same.\n", count := [ 2, 5, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[2,4,4,]],[1],[4]);;\ngap> IsDenseA\
utomaton(aut);\nfalse\ngap> y:=NullCompletionAutomaton(aut);;Display(y);\n   |\
  1  2  3  4  5\n--------------------\n a |  3  5  3  4  5\n b |  2  4  4  5  \
5\nInitial state:   [ 1 ]\nAccepting state: [ 4 ]\n", count := [ 2, 5, 2, 4 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 5, 2, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 23731, 
                                                          root := ~, 
                                                          start := 23427, 
                                                          stop := 23730 ), 
                                                      rec( 
                                                          content := "\n\nThe \
state added is a ", count := [ 2, 5, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ink state", count := [ 2, 5, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Emph", 
                                                          next := 23777, 
                                                          root := ~, 
                                                          start := 23754, 
                                                          stop := 23776 ), 
                                                      rec( 
                                                          content := " i.e. it\
 is a state ", count := [ 2, 5, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "q\
", count := [ 2, 5, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 23805, 
                                                          root := ~, 
                                                          start := 23797, 
                                                          stop := 23804 ), 
                                                      rec( 
                                                          content := " which i\
s not initial nor accepting and for all letter ", count := [ 2, 5, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
", count := [ 2, 5, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 23868, 
                                                          root := ~, 
                                                          start := 23860, 
                                                          stop := 23867 ), 
                                                      rec( 
                                                          content := " in the \
alphabet of the automaton, ", count := [ 2, 5, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "q\
", count := [ 2, 5, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 23911, 
                                                          root := ~, 
                                                          start := 23903, 
                                                          stop := 23910 ), 
                                                      rec( 
                                                          content := " is the \
result of the action of ", count := [ 2, 5, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
", count := [ 2, 5, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 23951, 
                                                          root := ~, 
                                                          start := 23943, 
                                                          stop := 23950 ), 
                                                      rec( content := "  in ",
                                                          count := 
                                                            [ 2, 5, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "q\
", count := [ 2, 5, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 23964, 
                                                          root := ~, 
                                                          start := 23956, 
                                                          stop := 23963 ), 
                                                      rec( 
                                                          content := ". (Notic\
e that reading \na word, one does not go out of a sink state.) \n ", 
                                                          count := 
                                                            [ 2, 5, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 24050, root := ~, 
                                                  start := 23184, 
                                                  stop := 24049 ) ], 
                                          count := [ 2, 5, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 24064, root := ~, 
                                          start := 23121, stop := 24063 ), 
                                      rec( content := "  \n\n", 
                                          count := [ 2, 5, 2, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "ListSinkStatesA\
ut" ), content := 0, count := [ 2, 5, 3, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 24123, root := ~, 
                                                  start := 24081, 
                                                  stop := 24122 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nCompute\
s the list of all sink states of the automaton ", count := [ 2, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 24202, 
                                                          root := ~, 
                                                          start := 24192, 
                                                          stop := 24201 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=Automaton(\"det\",3,2,[ [ 2, 3, 3 ], [ 1, 2, 3 ] ],[ 1 ],[ 2, 3 ]);;\
\ngap> ListSinkStatesAut(x);\n[  ]\ngap> y:=Automaton(\"det\",3,2,[ [ 2, 3, 3 \
], [ 1, 2, 3 ] ],[ 1 ],[ 2 ]);;\ngap> ListSinkStatesAut(y);\n[ 3 ]\n", 
                                                                  count := 
                                                                    [ 2, 5, 
                                                                      3, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 5, 3, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 24448, 
                                                          root := ~, 
                                                          start := 24204, 
                                                          stop := 24447 ), 
                                                      rec( content := "\n ", 
                                                          count := 
                                                            [ 2, 5, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 24464, root := ~, 
                                                  start := 24124, 
                                                  stop := 24463 ) ], 
                                          count := [ 2, 5, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 24478, root := ~, 
                                          start := 24068, stop := 24477 ), 
                                      rec( content := "  \n\n", 
                                          count := [ 2, 5, 3, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "RemovedSinkStat\
es" ), content := 0, count := [ 2, 5, 4, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 24537, root := ~, 
                                                  start := 24495, 
                                                  stop := 24536 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nRemoves\
 all sink states of the automaton ", count := [ 2, 5, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 24603, 
                                                          root := ~, 
                                                          start := 24593, 
                                                          stop := 24602 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 5, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> y:=Automaton(\"det\",3,2,[[ 2, 3, 3 ],[ 1, 2, 3 ]],[ 1 ],[ 2 ]);;Display\
(y);\n   |  1  2  3\n--------------\n a |  2  3  3\n b |  1  2  3\nInitial sta\
te:   [ 1 ]\nAccepting state: [ 2 ]\ngap> x := RemovedSinkStates(y);Display(x)\
;\n< deterministic automaton on 2 letters with 2 states >\n   |  1  2\n-------\
----\n a |  2\n b |  1  2\nInitial state:   [ 1 ]\nAccepting state: [ 2 ]\n", 
                                                                  count := 
                                                                    [ 2, 5, 
                                                                      4, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 5, 4, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 25006, 
                                                          root := ~, 
                                                          start := 24605, 
                                                          stop := 25005 ), 
                                                      rec( content := "\n ", 
                                                          count := 
                                                            [ 2, 5, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 25022, root := ~, 
                                                  start := 24538, 
                                                  stop := 25021 ) ], 
                                          count := [ 2, 5, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 25036, root := ~, 
                                          start := 24482, stop := 25035 ), 
                                      rec( content := "  \n\n", 
                                          count := [ 2, 5, 4, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "ReversedAutomat\
on" ), content := 0, count := [ 2, 5, 5, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 25095, root := ~, 
                                                  start := 25053, 
                                                  stop := 25094 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nInverts\
 the arrows of the automaton ", count := [ 2, 5, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 25156, 
                                                          root := ~, 
                                                          start := 25146, 
                                                          stop := 25155 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> y:=Automaton(\"det\",3,2,[ [ 2, 3, 3 ], [ 1, 2, 3 ] ],[ 1 ],[ 2 ]);;\nga\
p> z:=ReversedAutomaton(y);;Display(z);\n   |  1       2       3\n------------\
------------------\n a |         [ 1 ]   [ 2, 3 ]\n b | [ 1 ]   [ 2 ]   [ 3 ]\
\nInitial state:   [ 2 ]\nAccepting state: [ 1 ]\n", count := [ 2, 5, 5, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 5, 5, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 25462, 
                                                          root := ~, 
                                                          start := 25158, 
                                                          stop := 25461 ), 
                                                      rec( content := "\n ", 
                                                          count := 
                                                            [ 2, 5, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 25478, root := ~, 
                                                  start := 25096, 
                                                  stop := 25477 ) ], 
                                          count := [ 2, 5, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 25492, root := ~, 
                                          start := 25040, stop := 25491 ), 
                                      rec( content := "  \n\n\n", 
                                          count := [ 2, 5, 5, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut, p", 
                                                      Name := "PermutedAutomat\
on" ), content := 0, count := [ 2, 5, 6, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 25555, root := ~, 
                                                  start := 25510, 
                                                  stop := 25554 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nGiven a\
n automaton ", count := [ 2, 5, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 5, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 25599, 
                                                          root := ~, 
                                                          start := 25589, 
                                                          stop := 25598 ), 
                                                      rec( 
                                                          content := " and a l\
ist ", count := [ 2, 5, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
", count := [ 2, 5, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 25619, 
                                                          root := ~, 
                                                          start := 25611, 
                                                          stop := 25618 ), 
                                                      rec( 
                                                          content := " represe\
nting a permutation of the states,\noutputs the equivalent permuted automaton.\
\n", count := [ 2, 5, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> y:=Automaton(\"det\",4,2,[[2,3,4,2],[0,0,0,1]],[1],[3]);;Display(y);\n  \
 |  1  2  3  4\n-----------------\n a |  2  3  4  2\n b |           1\nInitial\
 state:   [ 1 ]\nAccepting state: [ 3 ]\ngap> Display(PermutedAutomaton(y, [3,\
2,4,1]));\n   |  1  2  3  4\n-----------------\n a |  2  4  2  1\n b |  3\nIni\
tial state:   [ 3 ]\nAccepting state: [ 4 ]\n", count := [ 2, 5, 6, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 5, 6, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 26077, 
                                                          root := ~, 
                                                          start := 25705, 
                                                          stop := 26076 ), 
                                                      rec( content := "\n ", 
                                                          count := 
                                                            [ 2, 5, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 26093, root := ~, 
                                                  start := 25556, 
                                                  stop := 26092 ) ], 
                                          count := [ 2, 5, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 26107, root := ~, 
                                          start := 25497, stop := 26106 ), 
                                      rec( content := "  \n\n\n\n", 
                                          count := [ 2, 5, 6, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "ListPermutedAut\
omata" ), content := 0, count := [ 2, 5, 7, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 26171, root := ~, 
                                                  start := 26126, 
                                                  stop := 26170 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nGiven a\
n automaton ", count := [ 2, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 26215, 
                                                          root := ~, 
                                                          start := 26205, 
                                                          stop := 26214 ), 
                                                      rec( 
                                                          content := ", return\
s a list of automata with permuted states\n", count := [ 2, 5, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=Automaton(\"det\",3,2,[ [ 0, 2, 3 ], [ 1, 2, 3 ] ],[ 1 ],[ 2, 3 ]);;\
\ngap> ListPermutedAutomata(x);\n[ < deterministic automaton on 2 letters with\
 3 states >, \n  < deterministic automaton on 2 letters with 3 states >, \n  <\
 deterministic automaton on 2 letters with 3 states >, \n  < deterministic aut\
omaton on 2 letters with 3 states >, \n  < deterministic automaton on 2 letter\
s with 3 states >, \n  < deterministic automaton on 2 letters with 3 states > \
]\n", count := [ 2, 5, 7, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 2, 5, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 26756, 
                                                          root := ~, 
                                                          start := 26265, 
                                                          stop := 26755 ), 
                                                      rec( content := "\n ", 
                                                          count := 
                                                            [ 2, 5, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 26772, root := ~, 
                                                  start := 26172, 
                                                  stop := 26771 ) ], 
                                          count := [ 2, 5, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 26786, root := ~, 
                                          start := 26113, stop := 26785 ), 
                                      rec( content := " \n \n\n", 
                                          count := [ 2, 5, 7, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A", 
                                                      Name := "NormalizedAutom\
aton" ), content := 0, count := [ 2, 5, 8, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 26846, root := ~, 
                                                  start := 26804, 
                                                  stop := 26845 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nProduce\
s an equivalent automaton but in which the initial state is numbered 1 and the\
 accepting states have the greatest numbers.\n", count := [ 2, 5, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=Automaton(\"det\",3,2,[[ 1, 2, 0 ],[ 0, 1, 2 ]],[2],[1, 2]);;Display(\
x);\n   |  1  2  3\n--------------\n a |  1  2\n b |     1  2\nInitial state: \
   [ 2 ]\nAccepting states: [ 1, 2 ]\ngap> Display(NormalizedAutomaton(x));\n \
  |  1  2  3\n--------------\n a |  1     3\n b |  3  1\nInitial state:    [ 1\
 ]\nAccepting states: [ 3, 1 ]\n", count := [ 2, 5, 8, 4 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 27350, 
                                                          root := ~, 
                                                          start := 26991, 
                                                          stop := 27349 ), 
                                                      rec( content := "\n ", 
                                                          count := 
                                                            [ 2, 5, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 27366, root := ~, 
                                                  start := 26847, 
                                                  stop := 27365 ) ], 
                                          count := [ 2, 5, 8, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 27380, root := ~, 
                                          start := 26791, stop := 27379 ), 
                                      rec( content := "  \n\n", 
                                          count := [ 2, 5, 8, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A,B", 
                                                      Name := "UnionAutomata" 
                                                     ), content := 0, 
                                                  count := [ 2, 5, 9, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 27435, root := ~, 
                                                  start := 27397, 
                                                  stop := 27434 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nProduce\
s the disjoint union of the deterministic or non deterministic automata ", 
                                                          count := 
                                                            [ 2, 5, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 2, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 27537, 
                                                          root := ~, 
                                                          start := 27529, 
                                                          stop := 27536 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 2, 5, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
", count := [ 2, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 27550, 
                                                          root := ~, 
                                                          start := 27542, 
                                                          stop := 27549 ), 
                                                      rec( 
                                                          content := ". The ou\
tput is a non-deterministic automaton.\n", count := [ 2, 5, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=Automaton(\"det\",3,2,[ [ 1, 2, 0 ], [ 0, 1, 2 ] ],[ 2 ],[ 1, 2 ]);;\
\ngap> y:=Automaton(\"det\",3,2,[ [ 0, 1, 3 ], [ 0, 0, 0 ] ],[ 1 ],[ 1, 2, 3 ]\
);;\ngap> UnionAutomata(x,y);\n< non deterministic automaton on 2 letters with\
 6 states >\ngap> Display(last);\n   |  1       2       3       4    5       6\
\n------------------------------------------------\n a | [ 1 ]   [ 2 ]        \
        [ 4 ]   [ 6 ]\n b |         [ 1 ]   [ 2 ]\nInitial states:   [ 2, 4 ]\
\nAccepting states: [ 1, 2, 4, 5, 6 ]\n", count := [ 2, 5, 9, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 5, 9, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 28118, 
                                                          root := ~, 
                                                          start := 27597, 
                                                          stop := 28117 ), 
                                                      rec( content := "\n ", 
                                                          count := 
                                                            [ 2, 5, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 9, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 28134, root := ~, 
                                                  start := 27436, 
                                                  stop := 28133 ) ], 
                                          count := [ 2, 5, 9, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 28148, root := ~, 
                                          start := 27384, stop := 28147 ), 
                                      rec( content := "  \n\n", 
                                          count := [ 2, 5, 9, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A1,A2", 
                                                      Name := "ProductAutomato\
n" ), content := 0, count := [ 2, 5, 10, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 28209, root := ~, 
                                                  start := 28166, 
                                                  stop := 28208 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nThe arg\
uments must be deterministic automata. Returns the product of ", 
                                                          count := 
                                                            [ 2, 5, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
1", count := [ 2, 5, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 28302, 
                                                          root := ~, 
                                                          start := 28293, 
                                                          stop := 28301 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 2, 5, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
2", count := [ 2, 5, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 28316, 
                                                          root := ~, 
                                                          start := 28307, 
                                                          stop := 28315 ), 
                                                      rec( content := ". \n", 
                                                          count := 
                                                            [ 2, 5, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 2, 5, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 28323, 
                                                          root := ~, 
                                                          start := 28319, 
                                                          stop := 28322 ), 
                                                      rec( 
                                                          content := "\n Note:\
 ", count := [ 2, 5, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "(\
p,q)->(p-1)m+q", count := [ 2, 5, 10, 4 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 2, 5, 10, 4 ], mathmode := "Text", name := "M", 
                                                          next := 28353, 
                                                          root := ~, 
                                                          start := 28331, 
                                                          stop := 28352 ), 
                                                      rec( 
                                                          content := " is a bi\
jection from ", count := [ 2, 5, 10, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\{1,\\ldots, n\\}\\times \\{1,\\ldots, m\\}", count := [ 2, 5, 10, 4 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 2, 5, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 28418, 
                                                          root := ~, 
                                                          start := 28374, 
                                                          stop := 28417 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 2, 5, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\{1,\\ldots,mn\\}", count := [ 2, 5, 10, 4 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 2, 5, 10, 4 ], mathmode := "Text", 
                                                          name := "M", 
                                                          next := 28444, 
                                                          root := ~, 
                                                          start := 28422, 
                                                          stop := 28443 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 5, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=RandomAutomaton(\"det\",3,2);;Display(x);\n   |  1  2  3\n-----------\
---\n a |  2  3\n b |     1\nInitial state:    [ 3 ]\nAccepting states: [ 1, 2\
, 3 ]\ngap> y:=RandomAutomaton(\"det\",3,2);;Display(y);\n   |  1  2  3\n-----\
---------\n a |     1\n b |  1  3\nInitial state:    [ 3 ]\nAccepting states: \
[ 1, 3 ]\ngap> z:=ProductAutomaton(x, y);;Display(z);\n   |  1  2  3  4  5  6 \
 7  8  9\n--------------------------------\n a |     4        7\n b |         \
  1  3\nInitial state:    [ 9 ]\nAccepting states: [ 1, 3, 4, 6, 7, 9 ]\n", 
                                                                  count := 
                                                                    [ 2, 5, 
                                                                      10, 5 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 5, 10, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 28993, 
                                                          root := ~, 
                                                          start := 28446, 
                                                          stop := 28992 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 5, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 29008, root := ~, 
                                                  start := 28210, 
                                                  stop := 29007 ) ], 
                                          count := [ 2, 5, 10, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 29023, root := ~, 
                                          start := 28152, stop := 29022 ), 
                                      rec( content := " \n\n\n", 
                                          count := [ 2, 5, 10, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A1,A2", 
                                                      Name := "ProductOfLangua\
ges" ), content := 0, count := [ 2, 5, 11, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 29086, root := ~, 
                                                  start := 29041, 
                                                  stop := 29085 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nGiven t\
wo regular languages (as automata or rational expressions),\nreturns an automa\
ton that recognizes the concatenation of the given \nlanguages, that is, the s\
et of words ", count := [ 2, 5, 11, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
v", count := [ 2, 5, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 29283, 
                                                          root := ~, 
                                                          start := 29274, 
                                                          stop := 29282 ), 
                                                      rec( 
                                                          content := " such th\
at\n", count := [ 2, 5, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 2, 5, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 29302, 
                                                          root := ~, 
                                                          start := 29294, 
                                                          stop := 29301 ), 
                                                      rec( 
                                                          content := " belongs\
 to the first language and ", count := [ 2, 5, 11, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 2, 5, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 5, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 29345, 
                                                          root := ~, 
                                                          start := 29337, 
                                                          stop := 29344 ), 
                                                      rec( 
                                                          content := "\nbelong\
s to the second language.\n", count := [ 2, 5, 11, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> a1:=ListOfWordsToAutomaton(\"ab\",[\"aa\",\"bb\"]);\n< deterministic aut\
omaton on 2 letters with 5 states >\ngap> a2:=ListOfWordsToAutomaton(\"ab\",[\
\"a\",\"b\"]);\n< deterministic automaton on 2 letters with 3 states >\ngap> P\
roductOfLanguages(a1,a2);\n< deterministic automaton on 2 letters with 5 state\
s >\ngap> FAtoRatExp(last);\n(bbUaa)(aUb)\n", count := [ 2, 5, 11, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 5, 11, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 29743, 
                                                          root := ~, 
                                                          start := 29378, 
                                                          stop := 29742 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 5, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 11, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 29758, root := ~, 
                                                  start := 29087, 
                                                  stop := 29757 ) ], 
                                          count := [ 2, 5, 11, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 29773, root := ~, 
                                          start := 29027, stop := 29772 ), 
                                      rec( content := " \n\n\n", 
                                          count := [ 2, 5, 11, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 5, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 29787, 
                                  root := ~, start := 22907, stop := 29786 ), 
                              rec( content := "\n", count := [ 2, 5, 11, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Links with Semigr\
oups", count := [ 2, 6, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 2, 6, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 29837, 
                                          root := ~, start := 29797, 
                                          stop := 29836 ), 
                                      rec( 
                                          content := "\n\nEach letter of the a\
lphabet of an automaton induces a partial transformation in its set of \nstate\
s. The semigroup generated by these transformations is\ncalled the ", 
                                          count := [ 2, 6, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "transition semigr\
oup", count := [ 2, 6, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 2, 6, 0, 3 ], 
                                          mathmode := "Text", name := "E", 
                                          next := 30029, root := ~, 
                                          start := 30002, stop := 30028 ), 
                                      rec( content := " of the automaton.\n\n"
                                            , count := [ 2, 6, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "TransitionSemig\
roup" ), content := 0, count := [ 2, 6, 1, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 30107, root := ~, 
                                                  start := 30063, 
                                                  stop := 30106 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\nRetur\
ns the transition semigroup of the deterministic automaton ", 
                                                          count := 
                                                            [ 2, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 30197, 
                                                          root := ~, 
                                                          start := 30187, 
                                                          stop := 30196 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> aut := Automaton(\"det\",10,2,[[7,5,7,5,4,9,10,9,10,9],\n> [8,6,8,9,9,1,\
3,1,9,9]],[2],[6,7,8,9,10]);;\ngap> s := TransitionSemigroup(aut);;       \nga\
p> Size(s);                                                                  \
\n30\n", count := [ 2, 6, 1, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 2, 6, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 30462, 
                                                          root := ~, 
                                                          start := 30199, 
                                                          stop := 30461 ), 
                                                      rec( 
                                                          content := "\n\nThe \
transition semigroup of the minimal automaton recognizing a language is\nthe {\
\\it syntactic semigroup} of that language.\n\n ", count := [ 2, 6, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 6, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 30604, root := ~, 
                                                  start := 30108, 
                                                  stop := 30603 ) ], 
                                          count := [ 2, 6, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 30618, root := ~, 
                                          start := 30049, stop := 30617 ), 
                                      rec( content := "  \n", 
                                          count := [ 2, 6, 1, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut", 
                                                      Name := "SyntacticSemigr\
oupAut" ), content := 0, count := [ 2, 6, 2, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 30681, root := ~, 
                                                  start := 30635, 
                                                  stop := 30680 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\nRetur\
ns the syntactic semigroup of the  deterministic automaton ", 
                                                          count := 
                                                            [ 2, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 2, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 30771, 
                                                          root := ~, 
                                                          start := 30761, 
                                                          stop := 30770 ), 
                                                      rec( 
                                                          content := " (i.e. t\
he transition semigroup of the equivalent minimal automaton)\nwhen it is non e\
mpty and returns ", count := [ 2, 6, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 2, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 30884, 
                                                          root := ~, 
                                                          start := 30873, 
                                                          stop := 30883 ), 
                                                      rec( 
                                                          content := " otherwi\
se. \n", count := [ 2, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=Automaton(\"det\",3,2,[ [ 1, 2, 0 ], [ 0, 1, 2 ] ],[ 2 ],[ 1, 2 ]);;\
\ngap> S:=SyntacticSemigroupAut(x);;\ngap> Size(S);\n3\n", count := [ 2, 6, 
                                                                      2, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 6, 2, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 31055, 
                                                          root := ~, 
                                                          start := 30897, 
                                                          stop := 31054 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 6, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 6, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 31070, root := ~, 
                                                  start := 30682, 
                                                  stop := 31069 ) ], 
                                          count := [ 2, 6, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 31084, root := ~, 
                                          start := 30621, stop := 31083 ), 
                                      rec( content := " \n", 
                                          count := [ 2, 6, 2, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "rat", 
                                                      Name := "SyntacticSemigr\
oupLang" ), content := 0, count := [ 2, 6, 3, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 31147, root := ~, 
                                                  start := 31100, 
                                                  stop := 31146 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nReturns\
 the syntactic semigroup of the language given by the rational expression ", 
                                                          count := 
                                                            [ 2, 6, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
at", count := [ 2, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 6, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 31253, 
                                                          root := ~, 
                                                          start := 31243, 
                                                          stop := 31252 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 2, 6, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> rat := RationalExpression(\"a*ba*ba*(@Ub)\");;\ngap> S:=SyntacticSemigro\
upLang(rat);;\ngap> Size(S);\n7\n", count := [ 2, 6, 3, 4 ], name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 6, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 31391, 
                                                          root := ~, 
                                                          start := 31255, 
                                                          stop := 31390 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 2, 6, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 6, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 31406, root := ~, 
                                                  start := 31148, 
                                                  stop := 31405 ) ], 
                                          count := [ 2, 6, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 31420, root := ~, 
                                          start := 31086, stop := 31419 ), 
                                      rec( content := " \n", 
                                          count := [ 2, 6, 3, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 6, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 31432, 
                                  root := ~, start := 29788, stop := 31431 ), 
                              rec( content := "\n  ", count := [ 2, 6, 3, 5 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 2, 0, 0, 1 ], 
                          mathmode := "Text", name := "Chapter", 
                          next := 31445, root := ~, start := 7112, 
                          stop := 31444 ), 
                      rec( content := "\n\n\n\n", count := [ 2, 6, 3, 5 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := "xml version=\"1.0\" encoding=\"UTF-8\""
                            , count := [ 2, 6, 3, 5 ], mathmode := "Text", 
                          name := "XMLPI", root := ~ ), 
                      rec( content := "\n", count := [ 2, 6, 3, 5 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := " $Id: rational.xml,v 1.13  Exp $ ", 
                          count := [ 2, 6, 3, 5 ], mathmode := "Text", 
                          name := "XMLCOMMENT", root := ~ ), 
                      rec( content := "\n\n", count := [ 2, 6, 3, 5 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Rational languages", 
                                          count := [ 3, 0, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 0, 0, 2 ], mathmode := "Text",
                                  name := "Heading", next := 31576, 
                                  root := ~, start := 31539, stop := 31575 ), 
                              rec( 
                                  content := "\nRational languages are conveni\
ently represented through rational expressions. These are finite expressions i\
nvolving letters of the alphabet; ", count := [ 3, 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "concatenation", 
                                          count := [ 3, 0, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 0, 0, 3 ], mathmode := "Text",
                                  name := "C", next := 31739, root := ~, 
                                  start := 31719, stop := 31738 ), 
                              rec( content := ", corresponding to the ", 
                                  count := [ 3, 0, 0, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "product", 
                                          count := [ 3, 0, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 0, 0, 3 ], mathmode := "Text",
                                  name := "E", next := 31776, root := ~, 
                                  start := 31762, stop := 31775 ), 
                              rec( content := "; the symbol ", 
                                  count := [ 3, 0, 0, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "U", 
                                          count := [ 3, 0, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 0, 0, 3 ], mathmode := "Text",
                                  name := "C", next := 31797, root := ~, 
                                  start := 31789, stop := 31796 ), 
                              rec( content := ", corresponding to the ", 
                                  count := [ 3, 0, 0, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "union", 
                                          count := [ 3, 0, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 0, 0, 3 ], mathmode := "Text",
                                  name := "E", next := 31832, root := ~, 
                                  start := 31820, stop := 31831 ), 
                              rec( content := "; and  the symbol ", 
                                  count := [ 3, 0, 0, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "*", 
                                          count := [ 3, 0, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 0, 0, 3 ], mathmode := "Text",
                                  name := "C", next := 31858, root := ~, 
                                  start := 31850, stop := 31857 ), 
                              rec( 
                                  content := ", corresponding to the Kleene's \
star.\n", count := [ 3, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "rational expressions", 
                                          count := [ 3, 0, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 0, 0, 3 ], mathmode := "Text",
                                  name := "Index", next := 31931, root := ~, 
                                  start := 31896, stop := 31930 ), 
                              rec( content := "\n\n", count := [ 3, 0, 0, 3 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Rational Expressi\
ons", count := [ 3, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 3, 1, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 31981, 
                                          root := ~, start := 31942, 
                                          stop := 31980 ), 
                                      rec( content := "\nThe expressions ", 
                                          count := [ 3, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "@", 
                                                  count := [ 3, 1, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 1, 0, 3 ],
                                          mathmode := "Text", name := "C", 
                                          next := 32006, root := ~, 
                                          start := 31998, stop := 32005 ), 
                                      rec( content := " and ", 
                                          count := [ 3, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\"empty\\_set\"",
                                                  count := [ 3, 1, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 1, 0, 3 ],
                                          mathmode := "Text", name := "C", 
                                          next := 32030, root := ~, 
                                          start := 32011, stop := 32029 ), 
                                      rec( 
                                          content := " are used to represent t\
he empty word and the empty set respectively.\n\n\n ", 
                                          count := [ 3, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := " expr[, alph] ",
                                                      Name := "RationalExpress\
ion" ), content := 0, count := [ 3, 1, 1, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 32171, root := ~, 
                                                  start := 32117, 
                                                  stop := 32170 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nA ratio\
nal expression can be created using the function ", count := [ 3, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "R\
ationalExpression", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "C", 
                                                          next := 32267, 
                                                          root := ~, 
                                                          start := 32242, 
                                                          stop := 32266 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
xpr", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 32280, 
                                                          root := ~, 
                                                          start := 32269, 
                                                          stop := 32279 ), 
                                                      rec( 
                                                          content := " is a st\
ring representing the desired expression literally and ", count := 
                                                            [ 3, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
lph", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 32354, 
                                                          root := ~, 
                                                          start := 32343, 
                                                          stop := 32353 ), 
                                                      rec( 
                                                          content := " (may or\
 may not be present) is the alphabet of the expression. Of course ", 
                                                          count := 
                                                            [ 3, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
lph", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 32439, 
                                                          root := ~, 
                                                          start := 32428, 
                                                          stop := 32438 ), 
                                                      rec( 
                                                          content := " must no\
t contain the symbols '@', '(', ')', '*' nor 'U'. When ", count := 
                                                            [ 3, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
lph", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 32513, 
                                                          root := ~, 
                                                          start := 32502, 
                                                          stop := 32512 ), 
                                                      rec( 
                                                          content := " is not \
present, the alphabet of the rational expression is the set of symbols (other \
than '\"', etc...) occurring in the expression. (The alphabet is then ordered \
with the alphabetical order.)\n", count := [ 3, 1, 1, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> RationalExpression(\"abUc\");\nabUc\ngap> RationalExpression(\"ab*Uc\");\
\nab*Uc\ngap> RationalExpression(\"001U1*\");\n001U1*\ngap> RationalExpression\
(\"001U1*\",\"012\");\n001U1*\n", count := [ 3, 1, 1, 4 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 32906, 
                                                          root := ~, 
                                                          start := 32706, 
                                                          stop := 32905 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 3, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 32921, root := ~, 
                                                  start := 32172, 
                                                  stop := 32920 ) ], 
                                          count := [ 3, 1, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 32935, root := ~, 
                                          start := 32103, stop := 32934 ), 
                                      rec( content := "\n\n\n ", 
                                          count := [ 3, 1, 1, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := " n, operation, l\
ist ", Name := "RatExpOnnLetters" ), content := 0, count := [ 3, 1, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 33011, root := ~, 
                                                  start := 32953, 
                                                  stop := 33010 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nThis is\
 another way to construct a rational expression over an alphabet. The user may\
 specify the alphabet or just give the number ", count := [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 33165, 
                                                          root := ~, 
                                                          start := 33157, 
                                                          stop := 33164 ), 
                                                      rec( 
                                                          content := " of lett\
ers (in this case the alphabet ", count := [ 3, 1, 2, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\{a,b,c,\\ldots\\}", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 3, 1, 2, 3 ], mathmode := "Text", 
                                                          name := "M", 
                                                          next := 33227, 
                                                          root := ~, 
                                                          start := 33204, 
                                                          stop := 33226 ), 
                                                      rec( 
                                                          content := " is cons\
idered).  ", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
peration", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 33261, 
                                                          root := ~, 
                                                          start := 33245, 
                                                          stop := 33260 ), 
                                                      rec( 
                                                          content := " is the \
name of an operation, the possibilities\nbeing: ", count := [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
roduct", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 33330, 
                                                          root := ~, 
                                                          start := 33316, 
                                                          stop := 33329 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
nion", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 33344, 
                                                          root := ~, 
                                                          start := 33332, 
                                                          stop := 33343 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
tar", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 33359, 
                                                          root := ~, 
                                                          start := 33348, 
                                                          stop := 33358 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 33372, 
                                                          root := ~, 
                                                          start := 33361, 
                                                          stop := 33371 ), 
                                                      rec( 
                                                          content := " is a li\
st\n of rational expressions, a rational expression in the case of\n``star'', \
or a \nlist consisting of an integer when the rational expression is a single\
\nletter. The empty list ", count := [ 3, 1, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
  ]", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 33567, 
                                                          root := ~, 
                                                          start := 33556, 
                                                          stop := 33566 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
mpty\\_set", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 33589, 
                                                          root := ~, 
                                                          start := 33572, 
                                                          stop := 33588 ), 
                                                      rec( 
                                                          content := " are oth\
er possibilities for\n", count := [ 3, 1, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 33629, 
                                                          root := ~, 
                                                          start := 33618, 
                                                          stop := 33628 ), 
                                                      rec( 
                                                          content := ". \n\nAn\
 example follows\n", count := [ 3, 1, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> RatExpOnnLetters(2,\"star\",RatExpOnnLetters(2,\"product\",\n> [RatExpOn\
nLetters(2,[],[1]),RatExpOnnLetters(2,\"union\",\n> [RatExpOnnLetters(2,[],[1]\
),RatExpOnnLetters(2,[],[2])])]));      \n(a(aUb))*\n", count := [ 3, 1, 2, 4 
                                                                     ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 1, 2, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 33882, 
                                                          root := ~, 
                                                          start := 33652, 
                                                          stop := 33881 ), 
                                                      rec( 
                                                          content := "\n \nThe\
 empty word and the empty set are the rational expressions:\n", 
                                                          count := 
                                                            [ 3, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> RatExpOnnLetters(2,[],[]);         \n@\ngap> RatExpOnnLetters(2,[],\"emp\
ty_set\");\nempty_set\n", count := [ 3, 1, 2, 6 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 34074, 
                                                          root := ~, 
                                                          start := 33948, 
                                                          stop := 34073 ), 
                                                      rec( content := "\n ", 
                                                          count := 
                                                            [ 3, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 34090, root := ~, 
                                                  start := 33012, 
                                                  stop := 34089 ) ], 
                                          count := [ 3, 1, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 34103, root := ~, 
                                          start := 32939, stop := 34102 ), 
                                      rec( content := " \n\n", 
                                          count := [ 3, 1, 2, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "arg", 
                                                      Name := "RandomRatExp" )
                                                    , content := 0, 
                                                  count := [ 3, 1, 3, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 34157, root := ~, 
                                                  start := 34120, 
                                                  stop := 34156 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nGiven t\
he number of symbols of the alphabet and (possibly) a factor ", 
                                                          count := 
                                                            [ 3, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 34248, 
                                                          root := ~, 
                                                          start := 34240, 
                                                          stop := 34247 ), 
                                                      rec( 
                                                          content := " which i\
s intended to increase the randomality of the expression,\nreturns a pseudo ra\
ndom rational expression over that alphabet.\n", count := [ 3, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> RandomRatExp(2);\nb*(@Ua)\ngap> RandomRatExp(\"01\");\nempty_set\ngap> R\
andomRatExp(\"01\");\n(0U1)*\ngap> RandomRatExp(\"01\",7);\n0*1(@U0U1)\n", 
                                                                  count := 
                                                                    [ 3, 1, 
                                                                      3, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 1, 3, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 34545, 
                                                          root := ~, 
                                                          start := 34378, 
                                                          stop := 34544 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 3, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 34560, root := ~, 
                                                  start := 34158, 
                                                  stop := 34559 ) ], 
                                          count := [ 3, 1, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 34575, root := ~, 
                                          start := 34106, stop := 34574 ), 
                                      rec( content := " \n\n", 
                                          count := [ 3, 1, 3, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "r", 
                                                      Name := "SizeRatExp" ), 
                                                  content := 0, 
                                                  count := [ 3, 1, 4, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 34625, root := ~, 
                                                  start := 34592, 
                                                  stop := 34624 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nReturns\
 the size, i.e. the number of symbols of the alphabet, of the rational express\
ion ", count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
", count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 34737, 
                                                          root := ~, 
                                                          start := 34729, 
                                                          stop := 34736 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 3, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> a:=RationalExpression(\"0*1(@U0U1)\");\n0*1(@U0U1)\ngap> SizeRatExp(a);\
\n5\n", count := [ 3, 1, 4, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 34846, 
                                                          root := ~, 
                                                          start := 34739, 
                                                          stop := 34845 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 3, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 34861, root := ~, 
                                                  start := 34626, 
                                                  stop := 34860 ) ], 
                                          count := [ 3, 1, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 34876, root := ~, 
                                          start := 34578, stop := 34875 ), 
                                      rec( content := " \n\n", 
                                          count := [ 3, 1, 4, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "r", 
                                                      Name := "IsRationalExpre\
ssion" ), content := 0, count := [ 3, 1, 5, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 34936, root := ~, 
                                                  start := 34893, 
                                                  stop := 34935 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nTests w\
hether an object is a rational expression.\n", count := [ 3, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> r := RandomRatExp(\"01\",7);\n1(0U1)U@\ngap> IsRatExpOnnLettersObj(r) an\
d IsRationalExpressionRep(r);\ntrue\ngap> IsRationalExpression(RandomRatExp(\"\
01\"));\ntrue\n", count := [ 3, 1, 5, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 35193, 
                                                          root := ~, 
                                                          start := 35001, 
                                                          stop := 35192 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 3, 1, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 35208, root := ~, 
                                                  start := 34937, 
                                                  stop := 35207 ) ], 
                                          count := [ 3, 1, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 35223, root := ~, 
                                          start := 34879, stop := 35222 ), 
                                      rec( content := " \n\n", 
                                          count := [ 3, 1, 5, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "R", 
                                                      Name := "AlphabetOfRatEx\
p" ), content := 0, count := [ 3, 1, 6, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 35279, root := ~, 
                                                  start := 35240, 
                                                  stop := 35278 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\nRetur\
ns the number of symbols in the alphabet of the rational expression ", 
                                                          count := 
                                                            [ 3, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "R\
", count := [ 3, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 35376, 
                                                          root := ~, 
                                                          start := 35368, 
                                                          stop := 35375 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 3, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> r:=RandomRatExp(2);\na*(ba*U@)\ngap> AlphabetOfRatExp(r);\n2\ngap> r:=Ra\
ndomRatExp(\"01\");\n1*(01*U@)\ngap> AlphabetOfRatExp(r);\n2\ngap> a:=RandomTr\
ansformation(3);;\ngap> b:=RandomTransformation(3);;\ngap> r:=RandomRatExp([a,\
b]);\n(Transformation( [ 1, 1, 3 ] )UTransformation( [ 1, 1, 2 ] ))*\ngap> Alp\
habetOfRatExp(r);\n2\n", count := [ 3, 1, 6, 4 ], name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 35727, 
                                                          root := ~, 
                                                          start := 35378, 
                                                          stop := 35726 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 3, 1, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 35742, root := ~, 
                                                  start := 35280, 
                                                  stop := 35741 ) ], 
                                          count := [ 3, 1, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 35756, root := ~, 
                                          start := 35226, stop := 35755 ), 
                                      rec( content := "\n\n\n", 
                                          count := [ 3, 1, 6, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "R", 
                                                      Name := "AlphabetOfRatEx\
pAsList" ), content := 0, count := [ 3, 1, 7, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 35818, root := ~, 
                                                  start := 35773, 
                                                  stop := 35817 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\nRetur\
ns the alphabet of the rational expression ", count := [ 3, 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "R\
", count := [ 3, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 35890, 
                                                          root := ~, 
                                                          start := 35882, 
                                                          stop := 35889 ), 
                                                      rec( 
                                                          content := " always\\
nas a list.\nIf the alphabet of the rational expression is given by means of a\
n integer\nless than 27 it returns the list ", count := [ 3, 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
"abcd....\"", count := [ 3, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 36034, 
                                                          root := ~, 
                                                          start := 36017, 
                                                          stop := 36033 ), 
                                                      rec( 
                                                          content := ",\nother\
wise returns ", count := [ 3, 1, 7, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
 \"a1\", \"a2\", \"a3\", \"a4\", ... ]", count := [ 3, 1, 7, 3 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 36092, 
                                                          root := ~, 
                                                          start := 36054, 
                                                          stop := 36091 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 3, 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> r:=RandomRatExp(2);\n(aUb)((aUb)(bU@)U@)U@\ngap> AlphabetOfRatExpAsList(\
r);\n\"ab\"\ngap> r:=RandomRatExp(\"01\");\n1*(0U@)\ngap> AlphabetOfRatExpAsLi\
st(r);\n\"01\"\ngap> r:=RandomRatExp(30);;\ngap> AlphabetOfRatExpAsList(r);\n[\
 \"a1\", \"a2\", \"a3\", \"a4\", \"a5\", \"a6\", \"a7\", \"a8\", \"a9\", \"a10\
\", \"a11\", \n\"a12\", \"a13\", \"a14\", \"a15\", \"a16\", \"a17\", \"a18\", \
\"a19\", \"a20\", \"a21\", \n\"a22\", \"a23\", \"a24\", \"a25\", \"a26\", \"a2\
7\", \"a28\", \"a29\", \"a30\" ]\n", count := [ 3, 1, 7, 4 ], name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 36548, 
                                                          root := ~, 
                                                          start := 36094, 
                                                          stop := 36547 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 3, 1, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 36563, root := ~, 
                                                  start := 35819, 
                                                  stop := 36562 ) ], 
                                          count := [ 3, 1, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 36577, root := ~, 
                                          start := 35759, stop := 36576 ), 
                                      rec( content := "\n\n\n", 
                                          count := [ 3, 1, 7, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "R", 
                                                      Name := "CopyRatExp" ), 
                                                  content := 0, 
                                                  count := [ 3, 1, 8, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 36627, root := ~, 
                                                  start := 36594, 
                                                  stop := 36626 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nReturns\
 a new rational expression, which is a copy of ", count := [ 3, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "R\
", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 36704, 
                                                          root := ~, 
                                                          start := 36696, 
                                                          stop := 36703 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 3, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> r:=RandomRatExp(2);\na*(bU@)\ngap> CopyRatExp(r);\na*(bU@)\n", 
                                                                  count := 
                                                                    [ 3, 1, 
                                                                      8, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 1, 8, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 36799, 
                                                          root := ~, 
                                                          start := 36706, 
                                                          stop := 36798 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 3, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 36814, root := ~, 
                                                  start := 36628, 
                                                  stop := 36813 ) ], 
                                          count := [ 3, 1, 8, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 36828, root := ~, 
                                          start := 36580, stop := 36827 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 1, 8, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 1, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 36844, 
                                  root := ~, start := 31933, stop := 36843 ), 
                              rec( content := "\n\n", count := [ 3, 1, 8, 5 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Comparison of rat\
ional expressions", count := [ 3, 2, 0, 2 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 2, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 36908, 
                                          root := ~, start := 36855, 
                                          stop := 36907 ), 
                                      rec( 
                                          content := "\nThe way two rational e\
xpressions ", count := [ 3, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( attributes := rec(  ), 
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                                              rec( content := "r1", 
                                                  count := [ 3, 2, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 2, 0, 3 ],
                                          mathmode := "Text", name := "C", 
                                          next := 36951, root := ~, 
                                          start := 36942, stop := 36950 ), 
                                      rec( content := " and ", 
                                          count := [ 3, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "r2", 
                                                  count := [ 3, 2, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 2, 0, 3 ],
                                          mathmode := "Text", name := "C", 
                                          next := 36965, root := ~, 
                                          start := 36956, stop := 36964 ), 
                                      rec( 
                                          content := " are compared through th\
e\n", count := [ 3, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( 
                                          attributes := rec( Only := "LaTeX" )
                                            , 
                                          content := 
                                            [ 
                                              rec( content := "\n$<$\n", 
                                                  count := [ 3, 2, 0, 3 ], 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 2, 0, 3 ],
                                          mathmode := "Text", name := "Alt", 
                                          next := 37032, root := ~, 
                                          start := 36991, stop := 37031 ), 
                                      rec( content := "\n", 
                                          count := [ 3, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Only := "HTML" )
                                            , 
                                          content := 
                                            [ 
                                              rec( HTML := true, 
                                                  content := "\n<\n", 
                                                  count := [ 3, 2, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 2, 0, 3 ],
                                          name := "Alt", next := 37062, 
                                          root := ~, start := 37033, 
                                          stop := 37061 ), 
                                      rec( 
                                          content := " operator is the followi\
ng:\nthe empty set is lesser than everything else;\nif r1 and r2 are letters, \
then the lesser is taken from the order in the alphabet;\nif r1 is a letter an\
 r2 a product, union or star, then r1 is lesser than r2;\na star expression is\
 considered to be lesser than a product or union expression\nand a product les\
ser than a union;\nto compare two star expressions we compare the expressions \
under the stars;\nto compare two product or union expressions we compare the s\
ubexpressions of\neach expression from left to right;\n", 
                                          count := [ 3, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 2, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 37610, 
                                  root := ~, start := 36846, stop := 37609 ), 
                              rec( content := "\n\n\n", 
                                  count := [ 3, 2, 0, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Operations with r\
ational languages", count := [ 3, 3, 0, 2 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 3, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 37675, 
                                          root := ~, start := 37622, 
                                          stop := 37674 ), 
                                      rec( 
                                          content := "\n\nOnly operations with\
 rational languages over the same alphabet are allowed.\n", 
                                          count := [ 3, 3, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", name := "P", 
                                          next := 37757, root := ~, 
                                          start := 37753, stop := 37756 ), 
                                      rec( 
                                          content := "\nWe may compute express\
ions for the \n", count := [ 3, 3, 0, 4 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "product", 
                                                  count := [ 3, 3, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 3, 0, 4 ],
                                          mathmode := "Text", name := "C", 
                                          next := 37808, root := ~, 
                                          start := 37794, stop := 37807 ), 
                                      rec( content := ", ", 
                                          count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "union", 
                                                  count := [ 3, 3, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 3, 0, 4 ],
                                          mathmode := "Text", name := "C", 
                                          next := 37822, root := ~, 
                                          start := 37810, stop := 37821 ), 
                                      rec( content := " and ", 
                                          count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "star", 
                                                  count := [ 3, 3, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 3, 0, 4 ],
                                          mathmode := "Text", name := "C", 
                                          next := 37838, root := ~, 
                                          start := 37827, stop := 37837 ), 
                                      rec( 
                                          content := " (i.e.,\nsubmonoid gener\
ated by) of rational sets. In some cases,\nsimpler expressions representing th\
e same set are returned.    \nNote that that two simplifications are always ma\
de, namely,\n", count := [ 3, 3, 0, 4 ], mathmode := "Text", name := "PCDATA",
                                          root := ~ ), 
                                      rec( 
                                          attributes := rec( Only := "LaTeX" )
                                            , 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n$r\\cup\"empty_\
set\" = r$\n", count := [ 3, 3, 0, 4 ], name := "PCDATA", root := ~ ) ], 
                                          count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 38075, root := ~, 
                                          start := 38027, stop := 38074 ), 
                                      rec( content := "\n", 
                                          count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Only := "HTML" )
                                            , 
                                          content := 
                                            [ 
                                              rec( HTML := true, 
                                                  content := "\nrU\"empty_set\
\" = r\n", count := [ 3, 3, 0, 4 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 3, 3, 0, 4 ], 
                                          name := "Alt", next := 38118, 
                                          root := ~, start := 38076, 
                                          stop := 38117 ), 
                                      rec( content := "\n and \n", 
                                          count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          attributes := rec( Only := "LaTeX" )
                                            , 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n$r\\epsilon = r\
$\n", count := [ 3, 3, 0, 4 ], name := "PCDATA", root := ~ ) ], 
                                          count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 38166, root := ~, 
                                          start := 38125, stop := 38165 ), 
                                      rec( content := "\n", 
                                          count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Only := "HTML" )
                                            , 
                                          content := 
                                            [ 
                                              rec( HTML := true, 
                                                  content := "\nr@ = r\n", 
                                                  count := [ 3, 3, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 3, 0, 4 ],
                                          name := "Alt", next := 38198, 
                                          root := ~, start := 38167, 
                                          stop := 38197 ), 
                                      rec( 
                                          content := ".\n\n\nOf course, these \
operations may be used to construct more complex\nexpressions. \n\nFor rationa\
l expressions we have the functions ", count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "UnionRatExp", 
                                                  count := [ 3, 3, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 3, 0, 4 ],
                                          mathmode := "Text", name := "C", 
                                          next := 38348, root := ~, 
                                          start := 38330, stop := 38347 ), 
                                      rec( content := ", ", 
                                          count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "ProductRatExp", 
                                                  count := [ 3, 3, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 3, 0, 4 ],
                                          mathmode := "Text", name := "C", 
                                          next := 38370, root := ~, 
                                          start := 38350, stop := 38369 ), 
                                      rec( content := ", ", 
                                          count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "StarRatExp", 
                                                  count := [ 3, 3, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 3, 0, 4 ],
                                          mathmode := "Text", name := "C", 
                                          next := 38389, root := ~, 
                                          start := 38372, stop := 38388 ), 
                                      rec( 
                                          content := ", that return respective\
ly rational expressions for the ", count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "union", 
                                                  count := [ 3, 3, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 3, 0, 4 ],
                                          mathmode := "Text", name := "E", 
                                          next := 38457, root := ~, 
                                          start := 38445, stop := 38456 ), 
                                      rec( content := " and ", 
                                          count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "product", 
                                                  count := [ 3, 3, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 3, 0, 4 ],
                                          mathmode := "Text", name := "E", 
                                          next := 38476, root := ~, 
                                          start := 38462, stop := 38475 ), 
                                      rec( 
                                          content := " of \nthe languages give\
n by the rational expressions ", count := [ 3, 3, 0, 4 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "r", 
                                                  count := [ 3, 3, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 3, 0, 4 ],
                                          mathmode := "Text", name := "C", 
                                          next := 38537, root := ~, 
                                          start := 38529, stop := 38536 ), 
                                      rec( content := " and ", 
                                          count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "s", 
                                                  count := [ 3, 3, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 3, 0, 4 ],
                                          mathmode := "Text", name := "C", 
                                          next := 38550, root := ~, 
                                          start := 38542, stop := 38549 ), 
                                      rec( content := " and the ", 
                                          count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "star", 
                                                  count := [ 3, 3, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 3, 0, 4 ],
                                          mathmode := "Text", name := "C", 
                                          next := 38570, root := ~, 
                                          start := 38559, stop := 38569 ), 
                                      rec( 
                                          content := " of\nthe language given \
by the rational expression ", count := [ 3, 3, 0, 4 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "r", 
                                                  count := [ 3, 3, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 3, 0, 4 ],
                                          mathmode := "Text", name := "C", 
                                          next := 38628, root := ~, 
                                          start := 38620, stop := 38627 ), 
                                      rec( content := ".\n", 
                                          count := [ 3, 3, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "r,s", 
                                                      Name := "UnionRatExp" ),
                                                  content := 0, 
                                                  count := [ 3, 3, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 38680, root := ~, 
                                                  start := 38644, 
                                                  stop := 38679 ) ], 
                                          count := [ 3, 3, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 38695, root := ~, 
                                          start := 38630, stop := 38694 ), 
                                      rec( content := " \n\n ", 
                                          count := [ 3, 3, 1, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "r,s", 
                                                      Name := "ProductRatExp" 
                                                     ), content := 0, 
                                                  count := [ 3, 3, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 38751, root := ~, 
                                                  start := 38713, 
                                                  stop := 38750 ) ], 
                                          count := [ 3, 3, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 38766, root := ~, 
                                          start := 38699, stop := 38765 ), 
                                      rec( content := " \n\n ", 
                                          count := [ 3, 3, 2, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "r", 
                                                      Name := " StarRatExp" ),
                                                  content := 0, 
                                                  count := [ 3, 3, 3, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 38818, root := ~, 
                                                  start := 38784, 
                                                  stop := 38817 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\n\nThe\
 expression ", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "(\
a(aUb))*", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 38866, 
                                                          root := ~, 
                                                          start := 38850, 
                                                          stop := 38865 ), 
                                                      rec( 
                                                          content := " may be \
produced in the following way\n", count := [ 3, 3, 3, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> r1 := RatExpOnnLetters(2,[],[1]); \na\ngap> r2 := RatExpOnnLetters(2,[],\
[2]);\nb\ngap> r3 := UnionRatExp(r1,r2);\naUb\ngap> r4 := ProductRatExp(r1,r3)\
;\na(aUb)\ngap> r5 := StarRatExp(r4);\n(a(aUb))*\n", count := [ 3, 3, 3, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 3, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 39131, 
                                                          root := ~, 
                                                          start := 38904, 
                                                          stop := 39130 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 3, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 39146, root := ~, 
                                                  start := 38819, 
                                                  stop := 39145 ) ], 
                                          count := [ 3, 3, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 39159, root := ~, 
                                          start := 38770, stop := 39158 ), 
                                      rec( content := " \n", 
                                          count := [ 3, 3, 3, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 3, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 39171, 
                                  root := ~, start := 37613, stop := 39170 ), 
                              rec( content := "\n  ", count := [ 3, 3, 3, 5 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 3, 0, 0, 1 ], 
                          mathmode := "Text", name := "Chapter", 
                          next := 39184, root := ~, start := 31530, 
                          stop := 39183 ), 
                      rec( content := "\n\n\n", count := [ 3, 3, 3, 5 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := "xml version=\"1.0\" encoding=\"UTF-8\""
                            , count := [ 3, 3, 3, 5 ], mathmode := "Text", 
                          name := "XMLPI", root := ~ ), 
                      rec( content := "\n", count := [ 3, 3, 3, 5 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := " $Id: aut-vs-rat.xml,v 1.13  Exp $ ", 
                          count := [ 3, 3, 3, 5 ], mathmode := "Text", 
                          name := "XMLCOMMENT", root := ~ ), 
                      rec( content := "\n\n", count := [ 3, 3, 3, 5 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Automata ", 
                                          count := [ 4, 0, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "versus", 
                                                  count := [ 4, 0, 0, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 4, 0, 0, 2 ],
                                          mathmode := "Text", name := "Emph", 
                                          next := 39316, root := ~, 
                                          start := 39297, stop := 39315 ), 
                                      rec( content := " rational expressions",
                                          count := [ 4, 0, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 4, 0, 0, 2 ], mathmode := "Text",
                                  name := "Heading", next := 39347, 
                                  root := ~, start := 39279, stop := 39346 ), 
                              rec( 
                                  content := "\n\n\nA remarkable theorem due t\
o Kleene shows that a language is recognized by a finite automaton precisely w\
hen it may be given by means of a rational expression, i.e. is a rational lang\
uage.\n", count := [ 4, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 4, 0, 0, 4 ], mathmode := "Text",
                                  name := "P", next := 39542, root := ~, 
                                  start := 39538, stop := 39541 ), 
                              rec( 
                                  content := "\nAn automaton and a rational ex\
pression are said to be ", count := [ 4, 0, 0, 4 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "equivalent", 
                                          count := [ 4, 0, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 4, 0, 0, 4 ], mathmode := "Text",
                                  name := "E", next := 39614, root := ~, 
                                  start := 39597, stop := 39613 ), 
                              rec( 
                                  content := " when both represent the same la\
nguage.\nIn this chapter we describe functions to go from automata to equivale\
nt rational expressions and ", count := [ 4, 0, 0, 4 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "vice-versa", 
                                          count := [ 4, 0, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 4, 0, 0, 4 ], mathmode := "Text",
                                  name := "E", next := 39768, root := ~, 
                                  start := 39751, stop := 39767 ), 
                              rec( content := ".\n\n", 
                                  count := [ 4, 0, 0, 4 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "From automata to \
rational expressions", count := [ 4, 1, 0, 2 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 4, 1, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 39836, 
                                          root := ~, start := 39780, 
                                          stop := 39835 ), 
                                      rec( content := "\n\n\n", 
                                          count := [ 4, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A", 
                                                      Name := "AutomatonToRatE\
xp " ), content := 0, count := [ 4, 1, 1, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 39894, root := ~, 
                                                  start := 39853, 
                                                  stop := 39893 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A", 
                                                      Name := "AutToRatExp" ),
                                                  content := 0, 
                                                  count := [ 4, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 39929, root := ~, 
                                                  start := 39895, 
                                                  stop := 39928 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A", 
                                                      Name := "FAtoRatExp" ), 
                                                  content := 0, 
                                                  count := [ 4, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 39963, root := ~, 
                                                  start := 39930, 
                                                  stop := 39962 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n From a\
 finite automaton, ", count := [ 4, 1, 1, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "F\
AtoRatExp", count := [ 4, 1, 1, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 40021, 
                                                          root := ~, 
                                                          start := 40004, 
                                                          stop := 40020 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 4, 1, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
utToRatExp", count := [ 4, 1, 1, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 40041, 
                                                          root := ~, 
                                                          start := 40023, 
                                                          stop := 40040 ), 
                                                      rec( 
                                                          content := "  and ",
                                                          count := 
                                                            [ 4, 1, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
utomatonToRatExp", count := [ 4, 1, 1, 7 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 4, 1, 1, 7 ], mathmode := "Text", name := "C", 
                                                          next := 40071, 
                                                          root := ~, 
                                                          start := 40047, 
                                                          stop := 40070 ), 
                                                      rec( 
                                                          content := ", which \
are synonyms, compute one equivalent rational expression,\nusing the state eli\
mination algorithm.\n", count := [ 4, 1, 1, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=Automaton(\"det\",4,2,[[ 0, 1, 2, 3 ],[ 0, 1, 2, 3 ]],[ 3 ],[ 1, 3, 4\
 ]);;\ngap> FAtoRatExp(x);\n(aUb)(aUb)U@\ngap> aut:=Automaton(\"det\",4,\"xy\"\
,[[ 0, 1, 2, 3 ],[ 0, 1, 2, 3 ]],[ 3 ],[ 1, 3, 4 ]);;\ngap> FAtoRatExp(aut);\n\
(xUy)(xUy)U@\n", count := [ 4, 1, 1, 8 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 4, 1, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 40431, 
                                                          root := ~, 
                                                          start := 40176, 
                                                          stop := 40430 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 4, 1, 1, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 4, 1, 1, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 40446, root := ~, 
                                                  start := 39964, 
                                                  stop := 40445 ) ], 
                                          count := [ 4, 1, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 40461, root := ~, 
                                          start := 39839, stop := 40460 ), 
                                      rec( content := " \n", 
                                          count := [ 4, 1, 1, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 4, 1, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 40473, 
                                  root := ~, start := 39771, stop := 40472 ), 
                              rec( content := "\n", count := [ 4, 1, 1, 9 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "From rational exp\
ression to automata", count := [ 4, 2, 0, 2 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 4, 2, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 40538, 
                                          root := ~, start := 40483, 
                                          stop := 40537 ), 
                                      rec( content := "\n\n", 
                                          count := [ 4, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "R", 
                                                      Name := "RatExpToNDAut" 
                                                     ), content := 0, 
                                                  count := [ 4, 2, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 40590, root := ~, 
                                                  start := 40554, 
                                                  stop := 40589 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nGiven a\
 rational expression ", count := [ 4, 2, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "R\
", count := [ 4, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 40641, 
                                                          root := ~, 
                                                          start := 40633, 
                                                          stop := 40640 ), 
                                                      rec( 
                                                          content := ", comput\
es the equivalent NFA\n", count := [ 4, 2, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> r:=RationalExpression(\"aUab\");\naUab\ngap> Display(RatExpToNDAut(r));\
\n   |  1    2       3    4\n--------------------------------\n a |           \
        [ 1, 2 ]\n b |      [ 3 ]\nInitial state:    [ 4 ]\nAccepting states: \
[ 1, 3 ]\ngap> r:=RationalExpression(\"xUxy\"); \nxUxy\ngap> Display(RatExpToN\
DAut(r));    \n   |  1    2       3    4\n--------------------------------\n x\
 |                   [ 1, 2 ]   \n y |      [ 3 ]                   \nInitial \
state:    [ 4 ]\nAccepting states: [ 1, 3 ]\n", count := [ 4, 2, 1, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 2, 1, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 41180, 
                                                          root := ~, 
                                                          start := 40671, 
                                                          stop := 41179 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 4, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 4, 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 41195, root := ~, 
                                                  start := 40591, 
                                                  stop := 41194 ) ], 
                                          count := [ 4, 2, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 41210, root := ~, 
                                          start := 40540, stop := 41209 ), 
                                      rec( content := " \n\n", 
                                          count := [ 4, 2, 1, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "R", 
                                                      Name := "RatExpToAutomat\
on" ), content := 0, count := [ 4, 2, 2, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 41267, root := ~, 
                                                  start := 41227, 
                                                  stop := 41266 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "R", 
                                                      Name := "RatExpToAut" ),
                                                  content := 0, 
                                                  count := [ 4, 2, 2, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 41302, root := ~, 
                                                  start := 41268, 
                                                  stop := 41301 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n Given \
a rational expression ", count := [ 4, 2, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "R\
", count := [ 4, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 41354, 
                                                          root := ~, 
                                                          start := 41346, 
                                                          stop := 41353 ), 
                                                      rec( 
                                                          content := ", these \
functions, which are synonyms, use ", count := [ 4, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "RatExpT\
oNDAut" ), content := 0, count := [ 4, 2, 2, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 41424, 
                                                          root := ~, 
                                                          start := 41397, 
                                                          stop := 41423 ), 
                                                      rec( 
                                                          content := ") to com\
pute the equivalent NFA and then returns the equivalent minimal DFA\n", 
                                                          count := 
                                                            [ 4, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> r:=RationalExpression(\"@U(aUb)(aUb)\");\n@U(aUb)(aUb)\ngap> Display(Rat\
ExpToAut(r));\n   |  1  2  3  4\n-----------------\n a |  3  1  3  2\n b |  3 \
 1  3  2\nInitial state:    [ 4 ]\nAccepting states: [ 1, 4 ]\ngap> r:=Rationa\
lExpression(\"@U(0U1)(0U1)\");\n@U(0U1)(0U1)\ngap> Display(RatExpToAut(r));   \
           \n   |  1  2  3  4  \n-----------------\n 0 |  3  1  3  2  \n 1 |  \
3  1  3  2  \nInitial state:    [ 4 ]\nAccepting states: [ 1, 4 ]\n", 
                                                                  count := 
                                                                    [ 4, 2, 
                                                                      2, 6 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 2, 2, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 41954, 
                                                          root := ~, 
                                                          start := 41500, 
                                                          stop := 41953 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 4, 2, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 4, 2, 2, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 41969, root := ~, 
                                                  start := 41303, 
                                                  stop := 41968 ) ], 
                                          count := [ 4, 2, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 41984, root := ~, 
                                          start := 41213, stop := 41983 ), 
                                      rec( content := " \n\n", 
                                          count := [ 4, 2, 2, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 4, 2, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 41997, 
                                  root := ~, start := 40474, stop := 41996 ), 
                              rec( content := "\n ", count := [ 4, 2, 2, 7 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "\n    ", 
                                          count := [ 4, 3, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n      Some test\
s on automata\n    ", count := [ 4, 3, 0, 2 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 4, 3, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 42066, 
                                          root := ~, start := 42013, 
                                          stop := 42065 ), 
                                      rec( 
                                          content := "\n    This section descr\
ibes functions that perform tests on automata, rational expressions and their \
accepted languages.\n      ", count := [ 4, 3, 0, 3 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "R", 
                                                      Name := "IsEmptyLang" ),
                                                  content := 0, 
                                                  count := [ 4, 3, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 42249, root := ~, 
                                                  start := 42214, 
                                                  stop := 42248 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   This function tests if the language given through a rational expression or \
an automaton\n          ", count := [ 4, 3, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
n            R\n          ", count := [ 4, 3, 1, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 3, 1, 3 ], mathmode := "Text", 
                                                          name := "Arg", 
                                                          next := 42416, 
                                                          root := ~, 
                                                          start := 42380, 
                                                          stop := 42415 ), 
                                                      rec( 
                                                          content := "\n      \
    is the empty language.\n", count := [ 4, 3, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> r:=RandomRatExp(2);\nempty_set\ngap> IsEmptyLang(r);\ntrue\ngap> r:=Rand\
omRatExp(2);\naUb\ngap> IsEmptyLang(r);\nfalse\n", count := [ 4, 3, 1, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 3, 1, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 42587, 
                                                          root := ~, 
                                                          start := 42450, 
                                                          stop := 42586 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ 4, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 4, 3, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 42610, root := ~, 
                                                  start := 42258, 
                                                  stop := 42609 ) ], 
                                          count := [ 4, 3, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 42630, root := ~, 
                                          start := 42193, stop := 42629 ), 
                                      rec( content := "\n      ", 
                                          count := [ 4, 3, 1, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "R", 
                                                      Name := "IsFullLang" ), 
                                                  content := 0, 
                                                  count := [ 4, 3, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 42692, root := ~, 
                                                  start := 42658, 
                                                  stop := 42691 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   This function tests if the language given through a rational expression or \
an automaton\n          ", count := [ 4, 3, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
n            R\n          ", count := [ 4, 3, 2, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 3, 2, 3 ], mathmode := "Text", 
                                                          name := "Arg", 
                                                          next := 42859, 
                                                          root := ~, 
                                                          start := 42823, 
                                                          stop := 42858 ), 
                                                      rec( 
                                                          content := "\n      \
    represents the Kleene closure of the alphabet of\n          ", 
                                                          count := 
                                                            [ 4, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
n            R\n          ", count := [ 4, 3, 2, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 3, 2, 3 ], mathmode := "Text", 
                                                          name := "A", 
                                                          next := 42961, 
                                                          root := ~, 
                                                          start := 42929, 
                                                          stop := 42960 ), 
                                                      rec( 
                                                          content := "\n      \
    .\n", count := [ 4, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> r:=RationalExpression(\"aUb\");\naUb\ngap> IsFullLang(r);\nfalse\ngap> r\
:=RationalExpression(\"(aUb)*\");\n(aUb)*\ngap> IsFullLang(r);\ntrue\n", 
                                                                  count := 
                                                                    [ 4, 3, 
                                                                      2, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 3, 2, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 43129, 
                                                          root := ~, 
                                                          start := 42974, 
                                                          stop := 43128 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ 4, 3, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 4, 3, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 43152, root := ~, 
                                                  start := 42701, 
                                                  stop := 43151 ) ], 
                                          count := [ 4, 3, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 43172, root := ~, 
                                          start := 42637, stop := 43171 ), 
                                      rec( content := "\n\n\n", 
                                          count := [ 4, 3, 2, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A1, A2", 
                                                      Name := "AreEqualLang" )
                                                    , content := 0, 
                                                  count := [ 4, 3, 3, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 43238, root := ~, 
                                                  start := 43197, 
                                                  stop := 43237 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A1,A2 ", 
                                                      Name := "AreEquivAut" ),
                                                  content := 0, 
                                                  count := [ 4, 3, 3, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 43278, root := ~, 
                                                  start := 43239, 
                                                  stop := 43277 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n These \
functions, which are synonyms, test if the automata or rational expressions ",
                                                          count := 
                                                            [ 4, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
1", count := [ 4, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 4, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 43385, 
                                                          root := ~, 
                                                          start := 43376, 
                                                          stop := 43384 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 4, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
2", count := [ 4, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 4, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 43399, 
                                                          root := ~, 
                                                          start := 43390, 
                                                          stop := 43398 ), 
                                                      rec( 
                                                          content := " are equ\
ivalent, i.e. represent the same language. \nThis is performed by checking tha\
t the corresponding minimal automata are isomorphic. Note hat this cannot happ\
en if the alphabets are different.\n", count := [ 4, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> y:=RandomAutomaton(\"det\",4,2);;\ngap> x:=RandomAutomaton(\"det\",4,2);\
;\ngap> AreEquivAut(x, y);\nfalse\ngap> a:=RationalExpression(\"(aUb)*ab*\");\
\n(aUb)*ab*\ngap> b:=RationalExpression(\"(aUb)*\");\n(aUb)*\ngap> AreEqualLan\
g(a, b);\nfalse\ngap> a:=RationalExpression(\"(bUa)*\");\n(bUa)*\ngap> AreEqua\
lLang(a, b);\ntrue\ngap> x:=RationalExpression(\"(1U0)*\");\n(1U0)*\ngap> AreE\
qualLang(a, x);  \nThe given languages are not over the same alphabet\nfalse\n\
", count := [ 4, 3, 3, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 4, 3, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 44052, 
                                                          root := ~, 
                                                          start := 43597, 
                                                          stop := 44051 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ 4, 3, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 4, 3, 3, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 44075, root := ~, 
                                                  start := 43279, 
                                                  stop := 44074 ) ], 
                                          count := [ 4, 3, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 44095, root := ~, 
                                          start := 43175, stop := 44094 ), 
                                      rec( content := "\n      ", 
                                          count := [ 4, 3, 3, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "R1, R2", 
                                                      Name := "IsContainedLang\
" ), content := 0, count := [ 4, 3, 4, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 44167, root := ~, 
                                                  start := 44123, 
                                                  stop := 44166 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   Tests if the language represented  (through an automaton or a rational expr\
ession) by\n          ", count := [ 4, 3, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
n            R1\n          ", count := [ 4, 3, 4, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 3, 4, 3 ], mathmode := "Text", 
                                                          name := "A", 
                                                          next := 44329, 
                                                          root := ~, 
                                                          start := 44296, 
                                                          stop := 44328 ), 
                                                      rec( 
                                                          content := "\n      \
    is contained in the language represented (through an automaton or a ration\
al expression) by\n          ", count := [ 4, 3, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
n            R2\n          ", count := [ 4, 3, 4, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 3, 4, 3 ], mathmode := "Text", 
                                                          name := "A", 
                                                          next := 44475, 
                                                          root := ~, 
                                                          start := 44442, 
                                                          stop := 44474 ), 
                                                      rec( 
                                                          content := "\n      \
    .\n", count := [ 4, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> r:=RationalExpression(\"aUab\");\naUab\ngap> s:=RationalExpression(\"a\"\
,\"ab\");\na\ngap> IsContainedLang(s,r);\ntrue\ngap> IsContainedLang(r,s);\nfa\
lse\n", count := [ 4, 3, 4, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 4, 3, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 44654, 
                                                          root := ~, 
                                                          start := 44488, 
                                                          stop := 44653 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ 4, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 4, 3, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 44677, root := ~, 
                                                  start := 44176, 
                                                  stop := 44676 ) ], 
                                          count := [ 4, 3, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 44697, root := ~, 
                                          start := 44102, stop := 44696 ), 
                                      rec( content := "\n      ", 
                                          count := [ 4, 3, 4, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "R1, R2", 
                                                      Name := "AreDisjointLang\
" ), content := 0, count := [ 4, 3, 5, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 44769, root := ~, 
                                                  start := 44725, 
                                                  stop := 44768 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   Tests if the languages represented (through automata or a rational expressi\
ons) by\n          ", count := [ 4, 3, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
n            R1\n          ", count := [ 4, 3, 5, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 3, 5, 3 ], mathmode := "Text", 
                                                          name := "A", 
                                                          next := 44928, 
                                                          root := ~, 
                                                          start := 44895, 
                                                          stop := 44927 ), 
                                                      rec( 
                                                          content := "\n      \
    and\n          ", count := [ 4, 3, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
n            R2\n          ", count := [ 4, 3, 5, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 3, 5, 3 ], mathmode := "Text", 
                                                          name := "A", 
                                                          next := 44986, 
                                                          root := ~, 
                                                          start := 44953, 
                                                          stop := 44985 ), 
                                                      rec( 
                                                          content := "\n      \
    are disjoint.\n", count := [ 4, 3, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> r:=RationalExpression(\"aUab\");;\ngap> s:=RationalExpression(\"a\",\"ab\
\");;\ngap> AreDisjointLang(r,s);\nfalse\n", count := [ 4, 3, 5, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 3, 5, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 45140, 
                                                          root := ~, 
                                                          start := 45011, 
                                                          stop := 45139 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ 4, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 4, 3, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 45163, root := ~, 
                                                  start := 44778, 
                                                  stop := 45162 ) ], 
                                          count := [ 4, 3, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 45183, root := ~, 
                                          start := 44704, stop := 45182 ), 
                                      rec( content := "\n  ", 
                                          count := [ 4, 3, 5, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 4, 3, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 45196, 
                                  root := ~, start := 41999, stop := 45195 ), 
                              rec( content := "\n\n", count := [ 4, 3, 5, 5 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 4, 0, 0, 1 ], 
                          mathmode := "Text", name := "Chapter", 
                          next := 45208, root := ~, start := 39270, 
                          stop := 45207 ), 
                      rec( content := "\n\n", count := [ 4, 3, 5, 5 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := "xml version=\"1.0\" encoding=\"UTF-8\""
                            , count := [ 4, 3, 5, 5 ], mathmode := "Text", 
                          name := "XMLPI", root := ~ ), 
                      rec( content := "\n", count := [ 4, 3, 5, 5 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := " $Id: aut-func.xml,v 1.13  Exp $ ", 
                          count := [ 4, 3, 5, 5 ], mathmode := "Text", 
                          name := "XMLCOMMENT", root := ~ ), 
                      rec( content := "\n\n", count := [ 4, 3, 5, 5 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "Some functions involving \
automata", count := [ 5, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ) ], 
                                  count := [ 5, 0, 0, 2 ], mathmode := "Text",
                                  name := "Heading", next := 45352, 
                                  root := ~, start := 45300, stop := 45351 ), 
                              rec( 
                                  content := "\nThis chapter describes some fu\
nctions involving automata. It starts with functions to obtain equivalent auto\
mata of other type. Then the minimalization is considered.\n\n", 
                                  count := [ 5, 0, 0, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "From one type to \
another", count := [ 5, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 5, 1, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 45573, 
                                          root := ~, start := 45530, 
                                          stop := 45572 ), 
                                      rec( 
                                          content := "\nRecall that two automa\
ta are said to be equivalent when they recognize the same language.\nNext we h\
ave functions which have as input automata of one type and as output equivalen\
t automata of another type.\n\n", count := [ 5, 1, 0, 3 ], mathmode := "Text",
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A", 
                                                      Name := "EpsilonToNFA" )
                                                    , content := 0, 
                                                  count := [ 5, 1, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 45829, root := ~, 
                                                  start := 45794, 
                                                  stop := 45828 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 5, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 45852, 
                                                          root := ~, 
                                                          start := 45844, 
                                                          stop := 45851 ), 
                                                      rec( 
                                                          content := " is an a\
utomaton with ", count := [ 5, 1, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\epsilon", count := [ 5, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 45889, 
                                                          root := ~, 
                                                          start := 45874, 
                                                          stop := 45888 ), 
                                                      rec( 
                                                          content := "-transit\
ions. Returns a NFA\nrecognizing the same language.\n", count := 
                                                            [ 5, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=RandomAutomaton(\"epsilon\",3,2);;Display(x);\n   |  1          2    \
      3\n------------------------------------\n a | [ 2 ]      [ 3 ]      [ 2 \
]\n b | [ 1, 2 ]   [ 1, 2 ]   [ 1, 3 ]\n @ | [ 1, 2 ]   [ 1, 2 ]   [ 1, 2 ]\nI\
nitial states:   [ 2, 3 ]\nAccepting states: [ 1, 2, 3 ]\ngap> Display(Epsilon\
ToNFA(x));\n   |  1          2             3\n--------------------------------\
----------\n a | [ 1, 2 ]   [ 1, 2, 3 ]   [ 1, 2 ]\n b | [ 1, 2 ]   [ 1, 2 ]  \
    [ 1, 2, 3 ]\nInitial states:   [ 1, 2, 3 ]\nAccepting states: [ 1, 2, 3 ]\
\n", count := [ 5, 1, 1, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 46509, 
                                                          root := ~, 
                                                          start := 45948, 
                                                          stop := 46508 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 46524, root := ~, 
                                                  start := 45830, 
                                                  stop := 46523 ) ], 
                                          count := [ 5, 1, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 46539, root := ~, 
                                          start := 45780, stop := 46538 ), 
                                      rec( content := " \n\n\n", 
                                          count := [ 5, 1, 1, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A", 
                                                      Name := "EpsilonToNFASet\
" ), content := 0, count := [ 5, 1, 2, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 46595, root := ~, 
                                                  start := 46557, 
                                                  stop := 46594 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 5, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 46618, 
                                                          root := ~, 
                                                          start := 46610, 
                                                          stop := 46617 ), 
                                                      rec( 
                                                          content := " is an a\
utomaton with ", count := [ 5, 1, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\epsilon", count := [ 5, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 46655, 
                                                          root := ~, 
                                                          start := 46640, 
                                                          stop := 46654 ), 
                                                      rec( 
                                                          content := "-transit\
ions. Returns a NFA\nrecognizing the same language. This function differs from\
 ", count := [ 5, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Epsilon\
ToNFA" ), content := 0, count := [ 5, 1, 2, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 46767, 
                                                          root := ~, 
                                                          start := 46741, 
                                                          stop := 46766 ), 
                                                      rec( 
                                                          content := "\nin tha\
t it is faster for smaller automata, or automata with few\nepsilon transitions\
, but slower in the really hard cases.\n", count := [ 5, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 46904, root := ~, 
                                                  start := 46596, 
                                                  stop := 46903 ) ], 
                                          count := [ 5, 1, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 46919, root := ~, 
                                          start := 46543, stop := 46918 ), 
                                      rec( content := " \n\n\n\n", 
                                          count := [ 5, 1, 2, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A", 
                                                      Name := "EpsilonCompacte\
dAut" ), content := 0, count := [ 5, 1, 3, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 46980, root := ~, 
                                                  start := 46938, 
                                                  stop := 46979 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 47003, 
                                                          root := ~, 
                                                          start := 46995, 
                                                          stop := 47002 ), 
                                                      rec( 
                                                          content := " is an a\
utomaton with ", count := [ 5, 1, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\epsilon", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 47040, 
                                                          root := ~, 
                                                          start := 47025, 
                                                          stop := 47039 ), 
                                                      rec( 
                                                          content := "-transit\
ions. Returns an \n", count := [ 5, 1, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\epsilon", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 47081, 
                                                          root := ~, 
                                                          start := 47066, 
                                                          stop := 47080 ), 
                                                      rec( 
                                                          content := "NFA with\
\neach strongly-connected component of the\nepsilon-transitions digraph of ", 
                                                          count := 
                                                            [ 5, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 47170, 
                                                          root := ~, 
                                                          start := 47162, 
                                                          stop := 47169 ), 
                                                      rec( 
                                                          content := " identif\
ied with a single state and\nrecognizing the same language.\n", 
                                                          count := 
                                                            [ 5, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=RandomAutomaton(\"epsilon\",3,2);;Display(x);\n   |  1          2    \
      3\n------------------------------------\n a | [ 1, 2 ]   [ 1, 3 ]   [ 1,\
 2 ]\n b | [ 1, 2 ]   [ 1, 2 ]   [ 2, 3 ]\n @ |            [ 3 ]      [ 2 ]\nI\
nitial state:    [ 3 ]\nAccepting states: [ 1, 3 ]\ngap> Display(EpsilonCompac\
tedAut(x));\n   |  1          2\n-------------------------\n a | [ 1, 2 ]   [ \
1, 2 ]\n b | [ 1, 2 ]   [ 1, 2 ]\n @ |\nInitial state:    [ 2 ]\nAccepting sta\
tes: [ 1, 2 ]\n", count := [ 5, 1, 3, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 47733, 
                                                          root := ~, 
                                                          start := 47237, 
                                                          stop := 47732 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 47748, root := ~, 
                                                  start := 46981, 
                                                  stop := 47747 ) ], 
                                          count := [ 5, 1, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 47763, root := ~, 
                                          start := 46924, stop := 47762 ), 
                                      rec( content := " \n\n\n\n", 
                                          count := [ 5, 1, 3, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A", 
                                                      Name := "ReducedNFA" ), 
                                                  content := 0, 
                                                  count := [ 5, 1, 4, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 47815, root := ~, 
                                                  start := 47782, 
                                                  stop := 47814 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 5, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 47838, 
                                                          root := ~, 
                                                          start := 47830, 
                                                          stop := 47837 ), 
                                                      rec( 
                                                          content := " is a no\
n deterministic automaton (without ", count := [ 5, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\epsilon", count := [ 5, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 47896, 
                                                          root := ~, 
                                                          start := 47881, 
                                                          stop := 47895 ), 
                                                      rec( 
                                                          content := "-transit\
ions). Returns an \nNFA accepting\nthe same language as its input but with pos\
sibly fewer states (it \nquotients out\nby the smallest right-invariant partit\
ion of the states). A paper describing\nthe algorithm is in preparation.\n", 
                                                          count := 
                                                            [ 5, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=RandomAutomaton(\"nondet\",5,2);;Display(x);\n   |  1             2  \
              3             4             5\n---------------------------------\
-------------------------------------\n a | [ 1, 5 ]      [ 1, 2, 4, 5 ]   [ 1\
, 3, 5 ]   [ 3, 4, 5 ]   [ 4 ]\n b | [ 2, 3, 4 ]   [ 3 ]            [ 2, 3, 4 \
]   [ 2, 4, 5 ]   [ 3 ]\nInitial state:    [ 4 ]\nAccepting states: [ 1, 3, 4,\
 5 ]\ngap> Display(ReducedNFA(x));\n   |  1             2                3    \
   4\n--------------------------------------------------------\n a | [ 1, 3 ] \
     [ 1, 2, 3, 4 ]   [ 4 ]   [ 1, 3, 4 ]\n b | [ 1, 2, 4 ]   [ 1 ]           \
 [ 1 ]   [ 2, 3, 4 ]\nInitial state:    [ 4 ]\nAccepting states: [ 1, 3, 4 ]\n\
", count := [ 5, 1, 4, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 48845, 
                                                          root := ~, 
                                                          start := 48128, 
                                                          stop := 48844 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 48860, root := ~, 
                                                  start := 47816, 
                                                  stop := 48859 ) ], 
                                          count := [ 5, 1, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 48875, root := ~, 
                                          start := 47768, stop := 48874 ), 
                                      rec( content := " \n\n\n\n", 
                                          count := [ 5, 1, 4, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A", 
                                                      Name := "NFAtoDFA" ), 
                                                  content := 0, 
                                                  count := [ 5, 1, 5, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 48925, root := ~, 
                                                  start := 48894, 
                                                  stop := 48924 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nGiven a\
n NFA, these synonym functions, compute the equivalent DFA, using the powerset\
 construction,\naccording to the algorithm presented in the report of the AMoR\
E ", count := [ 5, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Key := "AMORE:95\
" ), content := 0, count := [ 5, 1, 5, 3 ], mathmode := "Text", 
                                                          name := "Cite", 
                                                          next := 49126, 
                                                          root := ~, 
                                                          start := 49104, 
                                                          stop := 49125 ), 
                                                      rec( 
                                                          content := " program\
. \nThe returned automaton is dense deterministic\n", count := [ 5, 1, 5, 3 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=RandomAutomaton(\"nondet\",3,2);;Display(x);\n   |  1       2    3\n-\
--------------------------\n a | [ 2 ]        [ 1, 3 ]\n b |              [ 2,\
 3 ]\nInitial states:   [ 1, 3 ]\nAccepting states: [ 1, 2 ]\ngap> Display(NFA\
toDFA(x));\n   |  1  2  3\n--------------\n a |  2  2  1\n b |  3  3  3\nIniti\
al state:    [ 1 ]\nAccepting states: [ 1, 2, 3 ]\n", count := [ 5, 1, 5, 4 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 5, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 49561, 
                                                          root := ~, 
                                                          start := 49183, 
                                                          stop := 49560 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 1, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 49576, root := ~, 
                                                  start := 48926, 
                                                  stop := 49575 ) ], 
                                          count := [ 5, 1, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 49591, root := ~, 
                                          start := 48880, stop := 49590 ), 
                                      rec( content := " \n\n\n", 
                                          count := [ 5, 1, 5, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A, s1, s2", 
                                                      Name := "FuseSymbolsAut"\
 ), content := 0, count := [ 5, 1, 6, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 49654, root := ~, 
                                                  start := 49609, 
                                                  stop := 49653 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nGiven a\
n automaton ", count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 49696, 
                                                          root := ~, 
                                                          start := 49688, 
                                                          stop := 49695 ), 
                                                      rec( 
                                                          content := " and int\
egers ", count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
1", count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 49719, 
                                                          root := ~, 
                                                          start := 49710, 
                                                          stop := 49718 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
2", count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 49733, 
                                                          root := ~, 
                                                          start := 49724, 
                                                          stop := 49732 ), 
                                                      rec( 
                                                          content := " which, \
returns an NFA\nobtained by replacing all transitions through ", 
                                                          count := 
                                                            [ 5, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
2", count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 49811, 
                                                          root := ~, 
                                                          start := 49802, 
                                                          stop := 49810 ), 
                                                      rec( 
                                                          content := " by tran\
sitions through ", count := [ 5, 1, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
1", count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 49844, 
                                                          root := ~, 
                                                          start := 49835, 
                                                          stop := 49843 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 5, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=RandomAutomaton(\"det\",3,2);;Display(x);\n   |  1  2  3\n-----------\
---\n a |  2  3\n b |     1\nInitial state:    [ 3 ]\nAccepting states: [ 1, 2\
, 3 ]\ngap> Display(FuseSymbolsAut(x,1,2));\n   |  1       2          3\n-----\
----------------------\n a | [ 2 ]   [ 1, 3 ]\nInitial state:    [ 3 ]\nAccept\
ing states: [ 1, 2, 3 ]\n", count := [ 5, 1, 6, 4 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 50199, 
                                                          root := ~, 
                                                          start := 49846, 
                                                          stop := 50198 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 1, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 50214, root := ~, 
                                                  start := 49655, 
                                                  stop := 50213 ) ], 
                                          count := [ 5, 1, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 50229, root := ~, 
                                          start := 49595, stop := 50228 ), 
                                      rec( content := " \n\n\n\n", 
                                          count := [ 5, 1, 6, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 5, 1, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 50244, 
                                  root := ~, start := 45521, stop := 50243 ), 
                              rec( content := "\n\n\n", 
                                  count := [ 5, 1, 6, 5 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Minimalization of\
 an automaton", count := [ 5, 2, 0, 2 ], mathmode := "Text", name := "PCDATA",
                                                  root := ~ ) ], 
                                          count := [ 5, 2, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 50305, 
                                          root := ~, start := 50256, 
                                          stop := 50304 ), 
                                      rec( 
                                          content := "\nThe algorithm used to \
minimalize a dense deterministic automaton (i.e., to\ncompute a dense minimal \
\nautomaton recognizing the same language) is based on an algorithm due to\nHo\
pcroft (see ", count := [ 5, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( 
                                          attributes := rec( Key := "AHU:74" )
                                            , content := 0, 
                                          count := [ 5, 2, 0, 3 ], 
                                          mathmode := "Text", name := "Cite", 
                                          next := 50513, root := ~, 
                                          start := 50493, stop := 50512 ), 
                                      rec( 
                                          content := "). It is well known (see\
 ", count := [ 5, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                        , 
                                      rec( attributes := rec( Key := "HU:69" )
                                            , content := 0, 
                                          count := [ 5, 2, 0, 3 ], 
                                          mathmode := "Text", name := "Cite", 
                                          next := 50557, root := ~, 
                                          start := 50538, stop := 50556 ), 
                                      rec( 
                                          content := ") that it suffices\nto r\
educe the automaton given and remove the inaccessible states. Again, the\ndocu\
mentation for the computer program AMoRE ", count := [ 5, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          attributes := 
                                            rec( Key := "AMORE:95" ), 
                                          content := 0, 
                                          count := [ 5, 2, 0, 3 ], 
                                          mathmode := "Text", name := "Cite", 
                                          next := 50720, root := ~, 
                                          start := 50698, stop := 50719 ), 
                                      rec( 
                                          content := " has been very useful.\n\
\n", count := [ 5, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                         ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A", 
                                                      Name := "UsefulAutomaton\
" ), content := 0, count := [ 5, 2, 1, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 50796, root := ~, 
                                                  start := 50758, 
                                                  stop := 50795 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nGiven a\
n automaton ", count := [ 5, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 5, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 50838, 
                                                          root := ~, 
                                                          start := 50830, 
                                                          stop := 50837 ), 
                                                      rec( 
                                                          content := " (determ\
inistic or not), outputs a dense DFA ", count := [ 5, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
", count := [ 5, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 50891, 
                                                          root := ~, 
                                                          start := 50883, 
                                                          stop := 50890 ), 
                                                      rec( 
                                                          content := " whose s\
tates are all reachable and such that ", count := [ 5, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 5, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 50945, 
                                                          root := ~, 
                                                          start := 50937, 
                                                          stop := 50944 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
", count := [ 5, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 50958, 
                                                          root := ~, 
                                                          start := 50950, 
                                                          stop := 50957 ), 
                                                      rec( 
                                                          content := " are equ\
ivalent.\n", count := [ 5, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=RandomAutomaton(\"det\",4,2);;Display(x);\n   |  1  2  3  4\n--------\
---------\n a |     3  4\n b |  1  4\nInitial state:    [ 3 ]\nAccepting state\
s: [ 2, 3, 4 ]\ngap> Display(UsefulAutomaton(x));\n   |  1  2  3\n------------\
--\n a |  2  3  3\n b |  3  3  3\nInitial state:    [ 1 ]\nAccepting states: [\
 1, 2 ]\n", count := [ 5, 2, 1, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 2, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 51311, 
                                                          root := ~, 
                                                          start := 50975, 
                                                          stop := 51310 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 51326, root := ~, 
                                                  start := 50797, 
                                                  stop := 51325 ) ], 
                                          count := [ 5, 2, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 51341, root := ~, 
                                          start := 50744, stop := 51340 ), 
                                      rec( content := " \n\n", 
                                          count := [ 5, 2, 1, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A", 
                                                      Name := "MinimalizedAut"\
 ), content := 0, count := [ 5, 2, 2, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 51395, root := ~, 
                                                  start := 51358, 
                                                  stop := 51394 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nReturns\
 the minimal automaton equivalent to ", count := [ 5, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 5, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 51462, 
                                                          root := ~, 
                                                          start := 51454, 
                                                          stop := 51461 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 5, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=RandomAutomaton(\"det\",4,2);;Display(x);\n   |  1  2  3  4\n--------\
---------\n a |     3  4\n b |  1  2  3\nInitial state:    [ 4 ]\nAccepting st\
ates: [ 2, 3, 4 ]\ngap> Display(MinimalizedAut(x));\n   |  1  2\n-----------\n\
 a |  2  2\n b |  2  2\nInitial state:   [ 1 ]\nAccepting state: [ 1 ]\n", 
                                                                  count := 
                                                                    [ 5, 2, 
                                                                      2, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 2, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 51785, 
                                                          root := ~, 
                                                          start := 51464, 
                                                          stop := 51784 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 51800, root := ~, 
                                                  start := 51396, 
                                                  stop := 51799 ) ], 
                                          count := [ 5, 2, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 51815, root := ~, 
                                          start := 51344, stop := 51814 ), 
                                      rec( content := " \n\n", 
                                          count := [ 5, 2, 2, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A", 
                                                      Name := " MinimalAutomat\
on" ), content := 0, count := [ 5, 2, 3, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 51872, root := ~, 
                                                  start := 51832, 
                                                  stop := 51871 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nReturns\
 the minimal automaton equivalent to ", count := [ 5, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 5, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 51939, 
                                                          root := ~, 
                                                          start := 51931, 
                                                          stop := 51938 ), 
                                                      rec( 
                                                          content := ", but st\
ores it so that\nfuture computations of this automaton just return the stored \
automaton.\n", count := [ 5, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=RandomAutomaton(\"det\",4,2);;Display(x);\n   |  1  2  3  4\n--------\
---------\n a |     2  4\n b |     3  4\nInitial state:    [ 4 ]\nAccepting st\
ates: [ 1, 2, 3 ]\ngap> Display(MinimalAutomaton(x));\n   |  1\n--------\n a |\
  1\n b |  1\nInitial state:   [ 1 ]\nAccepting state:\n", count := [ 5, 2, 
                                                                      3, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 3, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 52340, 
                                                          root := ~, 
                                                          start := 52035, 
                                                          stop := 52339 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 52355, root := ~, 
                                                  start := 51873, 
                                                  stop := 52354 ) ], 
                                          count := [ 5, 2, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 52370, root := ~, 
                                          start := 51818, stop := 52369 ), 
                                      rec( content := " \n\n", 
                                          count := [ 5, 2, 3, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "aut [, p]", 
                                                      Name := "AccessibleState\
s" ), content := 0, count := [ 5, 2, 4, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 52434, root := ~, 
                                                  start := 52387, 
                                                  stop := 52433 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nCompute\
s the list of states of the automaton ", count := [ 5, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 52504, 
                                                          root := ~, 
                                                          start := 52494, 
                                                          stop := 52503 ), 
                                                      rec( 
                                                          content := " \n whic\
h are accessible from state ", count := [ 5, 2, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 52547, 
                                                          root := ~, 
                                                          start := 52539, 
                                                          stop := 52546 ), 
                                                      rec( 
                                                          content := ". When "
                                                            , 
                                                          count := 
                                                            [ 5, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 52562, 
                                                          root := ~, 
                                                          start := 52554, 
                                                          stop := 52561 ), 
                                                      rec( 
                                                          content := " is not \
given, returns the states which are accessible from any initial state.\n", 
                                                          count := 
                                                            [ 5, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=RandomAutomaton(\"det\",4,2);;Display(x);\n   |  1  2  3  4\n--------\
---------\n a |     1  2  4\n b |     2  4\nInitial state:    [ 2 ]\nAccepting\
 states: [ 1, 2, 3 ]\ngap> AccessibleStates(x,3);\n[ 1, 2, 3, 4 ]\n", 
                                                                  count := 
                                                                    [ 5, 2, 
                                                                      4, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 4, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 52884, 
                                                          root := ~, 
                                                          start := 52641, 
                                                          stop := 52883 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 52899, root := ~, 
                                                  start := 52435, 
                                                  stop := 52898 ) ], 
                                          count := [ 5, 2, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 52914, root := ~, 
                                          start := 52373, stop := 52913 ), 
                                      rec( content := " \n\n", 
                                          count := [ 5, 2, 4, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A", 
                                                      Name := "AccessibleAutom\
aton" ), content := 0, count := [ 5, 2, 5, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 52973, root := ~, 
                                                  start := 52931, 
                                                  stop := 52972 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n If  ",
                                                          count := 
                                                            [ 5, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 5, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 53001, 
                                                          root := ~, 
                                                          start := 52993, 
                                                          stop := 53000 ), 
                                                      rec( 
                                                          content := " is a de\
terministic automaton, not necessarily dense, an \n equivalent dense determini\
stic accessible automaton is returned. \n (The function ", 
                                                          count := 
                                                            [ 5, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "U\
sefulAutomaton", count := [ 5, 2, 5, 3 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 53163, 
                                                          root := ~, 
                                                          start := 53141, 
                                                          stop := 53162 ), 
                                                      rec( 
                                                          content := " is call\
ed.)\n", count := [ 5, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 53180, 
                                                          root := ~, 
                                                          start := 53176, 
                                                          stop := 53179 ), 
                                                      rec( 
                                                          content := "\n If  "
                                                            , 
                                                          count := 
                                                            [ 5, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 5, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 53194, 
                                                          root := ~, 
                                                          start := 53186, 
                                                          stop := 53193 ), 
                                                      rec( 
                                                          content := " is not \
deterministic with a single initial state, an equivalent \n accessible automat\
on is returned.\n\n", count := [ 5, 2, 5, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=RandomAutomaton(\"det\",4,2);;Display(x);\n   |  1  2  3  4\n--------\
---------\n a |  1  3\n b |  1  3  4\nInitial state:    [ 2 ]\nAccepting state\
s: [ 3, 4 ]\ngap> Display(AccessibleAutomaton(x));\n   |  1  2  3  4\n--------\
---------\n a |  2  4  4  4\n b |  2  3  4  4\nInitial state:    [ 1 ]\nAccept\
ing states: [ 2, 3 ]\n", count := [ 5, 2, 5, 5 ], name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 53645, 
                                                          root := ~, 
                                                          start := 53296, 
                                                          stop := 53644 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 53660, root := ~, 
                                                  start := 52974, 
                                                  stop := 53659 ) ], 
                                          count := [ 5, 2, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 53675, root := ~, 
                                          start := 52917, stop := 53674 ), 
                                      rec( content := " \n\n", 
                                          count := [ 5, 2, 5, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A1,A2", 
                                                      Name := "IntersectionLan\
guage" ), content := 0, count := [ 5, 2, 6, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 53739, root := ~, 
                                                  start := 53692, 
                                                  stop := 53738 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A1,A2", 
                                                      Name := "IntersectionAut\
omaton" ), content := 0, count := [ 5, 2, 6, 4 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 53788, root := ~, 
                                                  start := 53740, 
                                                  stop := 53787 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nCompute\
s an automaton that recognizes the intersection of the languages given (throug\
h automata or rational expressions by) ", count := [ 5, 2, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
1", count := [ 5, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 53936, 
                                                          root := ~, 
                                                          start := 53927, 
                                                          stop := 53935 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 2, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
2", count := [ 5, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 53950, 
                                                          root := ~, 
                                                          start := 53941, 
                                                          stop := 53949 ), 
                                                      rec( 
                                                          content := ".\nWhen \
the arguments are deterministic automata, is the same as ProductAutomaton, but\
 works for all kinds of automata. Note that the language of the product of two\
 automata is precisely the intersection of the languages of the automata.\n", 
                                                          count := 
                                                            [ 5, 2, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> x:=RandomAutomaton(\"det\",3,2);;Display(x);\n   |  1  2  3\n-----------\
---\n a |  2  3\n b |     1\nInitial state:    [ 3 ]\nAccepting states: [ 1, 2\
, 3 ]\ngap> y:=RandomAutomaton(\"det\",3,2);;Display(y);\n   |  1  2  3\n-----\
---------\n a |     1\n b |  1  3\nInitial state:    [ 3 ]\nAccepting states: \
[ 1, 3 ]\ngap> Display(IntersectionLanguage(x,y));\n   |  1  2\n-----------\n \
a |  2  2\n b |  2  2\nInitial state:   [ 1 ]\nAccepting state: [ 1 ]\n", 
                                                                  count := 
                                                                    [ 5, 2, 
                                                                      6, 6 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 6, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 54654, 
                                                          root := ~, 
                                                          start := 54187, 
                                                          stop := 54653 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 2, 6, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 6, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 54669, root := ~, 
                                                  start := 53789, 
                                                  stop := 54668 ) ], 
                                          count := [ 5, 2, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 54684, root := ~, 
                                          start := 53678, stop := 54683 ), 
                                      rec( content := " \n\n\n", 
                                          count := [ 5, 2, 6, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "A", 
                                                      Name := "AutomatonAllPai\
rsPaths" ), content := 0, count := [ 5, 2, 7, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 54747, root := ~, 
                                                  start := 54702, 
                                                  stop := 54746 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nGiven a\
n automaton ", count := [ 5, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 5, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 54789, 
                                                          root := ~, 
                                                          start := 54781, 
                                                          stop := 54788 ), 
                                                      rec( 
                                                          content := ", with "
                                                            , 
                                                          count := 
                                                            [ 5, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 54804, 
                                                          root := ~, 
                                                          start := 54796, 
                                                          stop := 54803 ), 
                                                      rec( 
                                                          content := " states,\
 outputs a ", count := [ 5, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 54831, 
                                                          root := ~, 
                                                          start := 54823, 
                                                          stop := 54830 ), 
                                                      rec( content := " x ", 
                                                          count := 
                                                            [ 5, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 54842, 
                                                          root := ~, 
                                                          start := 54834, 
                                                          stop := 54841 ), 
                                                      rec( 
                                                          content := " matrix \
P,\nsuch that P[i][j] is the list of simple paths from state i to\nstate j in \
", count := [ 5, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 5, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 54934, 
                                                          root := ~, 
                                                          start := 54926, 
                                                          stop := 54933 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 5, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> a:=RandomAutomaton(\"det\",3,2);\n< deterministic automaton on 2 letters\
 with 3 states >\ngap> AutomatonAllPairsPaths(a);\n[ [ [ [ 1, 1 ] ], [  ], [  \
] ], [ [ [ 2, 1 ] ], [ [ 2, 2 ] ], [  ] ],\n  [ [ [ 3, 2, 1 ] ], [ [ 3, 2 ] ],\
 [ [ 3, 3 ] ] ] ]\ngap> Display(a);\n   |  1  2  3\n--------------\n a |     1\
  2\n b |  1  2  3\nInitial state:    [ 3 ]\nAccepting states: [ 1, 2 ]\n", 
                                                                  count := 
                                                                    [ 5, 2, 
                                                                      7, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 7, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 55338, 
                                                          root := ~, 
                                                          start := 54936, 
                                                          stop := 55337 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 2, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 55353, root := ~, 
                                                  start := 54748, 
                                                  stop := 55352 ) ], 
                                          count := [ 5, 2, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 55368, root := ~, 
                                          start := 54688, stop := 55367 ), 
                                      rec( content := " \n\n\n    ", 
                                          count := [ 5, 2, 7, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 5, 2, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 55386, 
                                  root := ~, start := 50247, stop := 55385 ), 
                              rec( content := "\n", count := [ 5, 2, 7, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 5, 0, 0, 1 ], 
                          mathmode := "Text", name := "Chapter", 
                          next := 55397, root := ~, start := 45291, 
                          stop := 55396 ), 
                      rec( content := "\n\n\n\n\n\n", count := [ 5, 2, 7, 5 ],
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := "xml version=\"1.0\" encoding=\"UTF-8\""
                            , count := [ 5, 2, 7, 5 ], mathmode := "Text", 
                          name := "XMLPI", root := ~ ), 
                      rec( content := "\n", count := [ 5, 2, 7, 5 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := " $Id: finitelang.xml,v 1.13  Exp $ ", 
                          count := [ 5, 2, 7, 5 ], mathmode := "Text", 
                          name := "XMLCOMMENT", root := ~ ), 
                      rec( content := "\n\n", count := [ 5, 2, 7, 5 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "Finite regular languages"
                                            , count := [ 6, 0, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 6, 0, 0, 2 ], mathmode := "Text",
                                  name := "Heading", next := 55538, 
                                  root := ~, start := 55495, stop := 55537 ), 
                              rec( 
                                  content := "\nThis chapter describes some fu\
nctions to deal with finite regular languages.\n\n", count := [ 6, 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Dealing with fini\
te regular languages", count := [ 6, 1, 0, 2 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 6, 1, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 55682, 
                                          root := ~, start := 55626, 
                                          stop := 55681 ), 
                                      rec( content := "\n\n", 
                                          count := [ 6, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "L", 
                                                      Name := "IsFiniteRegular\
Language" ), content := 0, count := [ 6, 1, 1, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 55744, root := ~, 
                                                  start := 55698, 
                                                  stop := 55743 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 6, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "L\
", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 55767, 
                                                          root := ~, 
                                                          start := 55759, 
                                                          stop := 55766 ), 
                                                      rec( 
                                                          content := " is an a\
utomaton or a rational expression. This function tests\nwhether its argument r\
epresents a finite language or not.\n", count := [ 6, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> RandomRatExp(2);\nb*(aU@)\ngap> IsFiniteRegularLanguage(last);\nfalse\ng\
ap> RandomRatExp(2);\naUbU@\ngap> IsFiniteRegularLanguage(last);\ntrue\n", 
                                                                  count := 
                                                                    [ 6, 1, 
                                                                      1, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 1, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 56061, 
                                                          root := ~, 
                                                          start := 55888, 
                                                          stop := 56060 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 6, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 56076, root := ~, 
                                                  start := 55745, 
                                                  stop := 56075 ) ], 
                                          count := [ 6, 1, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 56091, root := ~, 
                                          start := 55684, stop := 56090 ), 
                                      rec( content := " \n\n\n", 
                                          count := [ 6, 1, 1, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "L", 
                                                      Name := "FiniteRegularLa\
nguageToListOfWords" ), content := 0, count := [ 6, 1, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 56166, root := ~, 
                                                  start := 56109, 
                                                  stop := 56165 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 6, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "L\
", count := [ 6, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 56189, 
                                                          root := ~, 
                                                          start := 56181, 
                                                          stop := 56188 ), 
                                                      rec( 
                                                          content := " is an a\
utomaton or a rational expression. \nThis function outputs the recognized lang\
uage as a list of words.\n", count := [ 6, 1, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> r:=RationalExpression(\"aaUx(aUb)\");   \naaUx(aUb)\ngap>  FiniteRegular\
LanguageToListOfWords(r);\n[ \"aa\", \"xa\", \"xb\" ]\n", count := [ 6, 1, 2, 
                                                                      4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 2, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 56451, 
                                                          root := ~, 
                                                          start := 56299, 
                                                          stop := 56450 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 6, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 56466, root := ~, 
                                                  start := 56167, 
                                                  stop := 56465 ) ], 
                                          count := [ 6, 1, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 56481, root := ~, 
                                          start := 56095, stop := 56480 ), 
                                      rec( content := " \n\n\n", 
                                          count := [ 6, 1, 2, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "alph, L", 
                                                      Name := "ListOfWordsToAu\
tomaton" ), content := 0, count := [ 6, 1, 3, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 56550, root := ~, 
                                                  start := 56499, 
                                                  stop := 56549 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\nGiven a\
n alphabet ", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
lph", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 56594, 
                                                          root := ~, 
                                                          start := 56583, 
                                                          stop := 56593 ), 
                                                      rec( 
                                                          content := " (a list\
) and a list of\nwords ", count := [ 6, 1, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "L\
", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 56632, 
                                                          root := ~, 
                                                          start := 56624, 
                                                          stop := 56631 ), 
                                                      rec( 
                                                          content := " (a list\
 of lists), outputs an automaton\nthat recognizes the given list of words.\n",
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> ListOfWordsToAutomaton(\"ab\",[\"aaa\",\"bba\",\"\"]);\n< deterministic \
automaton on 2 letters with 6 states >\ngap> FAtoRatExp(last);\n(bbUaa)aU@\n",
                                                                  count := 
                                                                    [ 6, 1, 
                                                                      3, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 3, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 56887, 
                                                          root := ~, 
                                                          start := 56714, 
                                                          stop := 56886 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 6, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 56902, root := ~, 
                                                  start := 56551, 
                                                  stop := 56901 ) ], 
                                          count := [ 6, 1, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 56917, root := ~, 
                                          start := 56485, stop := 56916 ), 
                                      rec( content := " \n\n\n\n\n\n    ", 
                                          count := [ 6, 1, 3, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 6, 1, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 56938, 
                                  root := ~, start := 55617, stop := 56937 ), 
                              rec( content := "\n", count := [ 6, 1, 3, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 6, 0, 0, 1 ], 
                          mathmode := "Text", name := "Chapter", 
                          next := 56949, root := ~, start := 55486, 
                          stop := 56948 ), 
                      rec( content := "\n\n\n\n\n\n\n", 
                          count := [ 6, 1, 3, 5 ], mathmode := "Text", 
                          name := "PCDATA", root := ~ ) ], 
                  count := [ 0, 0, 4, 1 ], mathmode := "Text", 
                  name := "Body", next := 56963, root := ~, start := 3125, 
                  stop := 56962 ), 
              rec( content := "xml version=\"1.0\" encoding=\"UTF-8\"", 
                  count := [ 6, 1, 3, 5 ], mathmode := "Text", 
                  name := "XMLPI", root := ~ ), 
              rec( content := " $Id: graphs.xml,v 1.13  Exp $ ", 
                  count := [ 6, 1, 3, 5 ], mathmode := "Text", 
                  name := "XMLCOMMENT", root := ~ ), 
              rec( attributes := rec(  ), 
                  content := 
                    [ 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Directed graphs", 
                                  count := [ "A", 0, 0, 2 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "A", 0, 0, 2 ], 
                          mathmode := "Text", name := "Heading", 
                          next := 57087, root := ~, start := 57053, 
                          stop := 57086 ), 
                      rec( 
                          content := "\nAutomata are frequently described thro\
ugh directed labeled graphs. This appendix on directed graphs (digraphs) is de\
voted to some functions designed with the purpose of being used as auxiliary f\
unctions to deal with automata, but may have independent interest.\n\n\n", 
                          count := [ "A", 0, 0, 3 ], mathmode := "Text", 
                          name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Directed graphs", 
                                          count := [ "A", 1, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 1, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 57394, root := ~, start := 57360, 
                                  stop := 57393 ), 
                              rec( content := "\nA directed graph with ", 
                                  count := [ "A", 1, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "n", 
                                          count := [ "A", 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 1, 0, 3 ], 
                                  mathmode := "Text", name := "M", 
                                  next := 57425, root := ~, start := 57417, 
                                  stop := 57424 ), 
                              rec( 
                                  content := " vertices is represented by an a\
djacency list.\n\nFor example, the list ", count := [ "A", 1, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "G = [[2,4],[3],[1,4],[]]"
                                            , count := [ "A", 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 1, 0, 3 ], 
                                  mathmode := "Text", name := "C", 
                                  next := 57526, root := ~, start := 57495, 
                                  stop := 57525 ), 
                              rec( 
                                  content := " represents a directed graph wit\
h ", count := [ "A", 1, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "4 (= Length(G))", 
                                          count := [ "A", 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 1, 0, 3 ], 
                                  mathmode := "Text", name := "C", 
                                  next := 57582, root := ~, start := 57560, 
                                  stop := 57581 ), 
                              rec( 
                                  content := " vertices; the sublist in positi\
on ", count := [ "A", 1, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "i", 
                                          count := [ "A", 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 1, 0, 3 ], 
                                  mathmode := "Text", name := "C", 
                                  next := 57625, root := ~, start := 57617, 
                                  stop := 57624 ), 
                              rec( 
                                  content := " is the list of endpoints of the\
 edges beginning in vertex ", count := [ "A", 1, 0, 3 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "i", 
                                          count := [ "A", 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 1, 0, 3 ], 
                                  mathmode := "Text", name := "M", 
                                  next := 57692, root := ~, start := 57684, 
                                  stop := 57691 ), 
                              rec( content := ".\n    ", 
                                  count := [ "A", 1, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Only := "LaTeX" ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "\n      \\begin{figure}[h\
tbp] \\begin{center} \\leavevmode \\includegraphics[bb=0 0 132 299]{graph} \\e\
nd{center} \\label{fig:graph} \\end{figure}\n    ", count := [ "A", 1, 0, 3 ],
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 1, 0, 3 ], 
                                  mathmode := "Text", name := "Alt", 
                                  next := 57865, root := ~, start := 57698, 
                                  stop := 57864 ), 
                              rec( content := "\n    ", 
                                  count := [ "A", 1, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Only := "HTML" ), 
                                  content := 
                                    [ 
                                      rec( HTML := true, 
                                          content := "\n      <br><center><img\
 src=\"graph.gif\"></center><br>\n    ", count := [ "A", 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 1, 0, 3 ], name := "Alt", 
                                  next := 57999, root := ~, start := 57870, 
                                  stop := 57998 ), 
                              rec( content := "\n    ", 
                                  count := [ "A", 1, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ "A", 1, 0, 4 ], 
                                  mathmode := "Text", name := "P", 
                                  next := 58009, root := ~, start := 58004, 
                                  stop := 58008 ), 
                              rec( content := "\n\n", 
                                  count := [ "A", 1, 0, 4 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "n", 
                                              Name := "RandomDiGraph" ), 
                                          content := 0, 
                                          count := [ "A", 1, 1, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 58061, root := ~, 
                                          start := 58025, stop := 58060 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\nProduces a pseu\
do random digraph with ", count := [ "A", 1, 1, 3 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "n", 
                                                          count := 
                                                            [ "A", 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 58122, 
                                                  root := ~, start := 58114, 
                                                  stop := 58121 ), 
                                              rec( content := " vertices\n", 
                                                  count := [ "A", 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> Ra\
ndomDiGraph(4);\n[ [  ], [ 1, 2, 4 ], [  ], [  ] ]\n", count := 
                                                            [ "A", 1, 1, 4 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 58221, root := ~, 
                                                  start := 58132, 
                                                  stop := 58220 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "A", 1, 1, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 58236, root := ~, 
                                          start := 58062, stop := 58235 ) ], 
                                  count := [ "A", 1, 1, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 58251, root := ~, start := 58011, 
                                  stop := 58250 ), 
                              rec( content := " \n\n\n", 
                                  count := [ "A", 1, 1, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "DG,v", 
                                              Name := "VertexInDegree" ), 
                                          content := 0, 
                                          count := [ "A", 1, 2, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 58309, root := ~, 
                                          start := 58269, stop := 58308 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\nComputes the in\
 degree of the vertex ", count := [ "A", 1, 2, 3 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "v", 
                                                          count := 
                                                            [ "A", 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 58369, 
                                                  root := ~, start := 58361, 
                                                  stop := 58368 ), 
                                              rec( 
                                                  content := " of the directed\
 graph ", count := [ "A", 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "DG", 
                                                          count := 
                                                            [ "A", 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 58401, 
                                                  root := ~, start := 58392, 
                                                  stop := 58400 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> G:\
=RandomDiGraph(4);\n[ [ 1 ], [ 1, 2, 4 ], [  ], [ 1, 2, 3 ] ]\ngap> VertexInDe\
gree(G,2);\n2\n", count := [ "A", 1, 2, 4 ], name := "PCDATA", root := ~ ) ], 
                                                  count := [ "A", 1, 2, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 58530, root := ~, 
                                                  start := 58402, 
                                                  stop := 58529 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 2, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "A", 1, 2, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 58545, root := ~, 
                                          start := 58310, stop := 58544 ) ], 
                                  count := [ "A", 1, 2, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 58560, root := ~, start := 58255, 
                                  stop := 58559 ), 
                              rec( content := " \n\n\n", 
                                  count := [ "A", 1, 2, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "DG,v", 
                                              Name := "VertexOutDegree" ), 
                                          content := 0, 
                                          count := [ "A", 1, 3, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 58619, root := ~, 
                                          start := 58578, stop := 58618 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\nComputes the ou\
t degree of the vertex ", count := [ "A", 1, 3, 3 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "v", 
                                                          count := 
                                                            [ "A", 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 58680, 
                                                  root := ~, start := 58672, 
                                                  stop := 58679 ), 
                                              rec( 
                                                  content := " of the directed\
 graph ", count := [ "A", 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "DG", 
                                                          count := 
                                                            [ "A", 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 58712, 
                                                  root := ~, start := 58703, 
                                                  stop := 58711 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> G:\
=RandomDiGraph(4);\n[ [ 1 ], [ 1, 2, 4 ], [  ], [ 1, 2, 3 ] ]\ngap> VertexOutD\
egree(G,2);\n3\n", count := [ "A", 1, 3, 4 ], name := "PCDATA", root := ~ ) ],
                                                  count := [ "A", 1, 3, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 58842, root := ~, 
                                                  start := 58713, 
                                                  stop := 58841 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 3, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "A", 1, 3, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 58857, root := ~, 
                                          start := 58620, stop := 58856 ) ], 
                                  count := [ "A", 1, 3, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 58872, root := ~, start := 58564, 
                                  stop := 58871 ), 
                              rec( content := " \n\n\n", 
                                  count := [ "A", 1, 3, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "DG,v", 
                                              Name := "AutoVertexDegree" ), 
                                          content := 0, 
                                          count := [ "A", 1, 4, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 58932, root := ~, 
                                          start := 58890, stop := 58931 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\nComputes the de\
gree of the vertex ", count := [ "A", 1, 4, 3 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "v", 
                                                          count := 
                                                            [ "A", 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 58989, 
                                                  root := ~, start := 58981, 
                                                  stop := 58988 ), 
                                              rec( 
                                                  content := " of the directed\
 graph ", count := [ "A", 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "DG", 
                                                          count := 
                                                            [ "A", 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 59021, 
                                                  root := ~, start := 59012, 
                                                  stop := 59020 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> G:\
=RandomDiGraph(4);\n[ [ 1 ], [ 1, 2, 4 ], [  ], [ 1, 2, 3 ] ]\ngap> AutoVertex\
Degree(G,2);\n5\n", count := [ "A", 1, 4, 4 ], name := "PCDATA", root := ~ ) ]
                                                    , 
                                                  count := [ "A", 1, 4, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 59152, root := ~, 
                                                  start := 59022, 
                                                  stop := 59151 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 4, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "A", 1, 4, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 59167, root := ~, 
                                          start := 58933, stop := 59166 ) ], 
                                  count := [ "A", 1, 4, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 59182, root := ~, start := 58876, 
                                  stop := 59181 ), 
                              rec( content := " \n\n\n\n\n", 
                                  count := [ "A", 1, 4, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "G", 
                                              Name := "ReversedGraph" ), 
                                          content := 0, 
                                          count := [ "A", 1, 5, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 59238, root := ~, 
                                          start := 59202, stop := 59237 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\nComputes the re\
versed graph of the directed graph G. It is the graph \nobtained from G by rev\
ersing the edges.\n", count := [ "A", 1, 5, 3 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> G:\
=RandomDiGraph(4);\n[ [  ], [ 4 ], [ 2 ], [ 1, 4 ] ]\ngap> ReversedGraph(G);\n\
[ [ 4 ], [ 3 ], [  ], [ 2, 4 ] ]\n", count := [ "A", 1, 5, 4 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 5, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 59510, root := ~, 
                                                  start := 59363, 
                                                  stop := 59509 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 5, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "A", 1, 5, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 59525, root := ~, 
                                          start := 59239, stop := 59524 ) ], 
                                  count := [ "A", 1, 5, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 59540, root := ~, start := 59188, 
                                  stop := 59539 ), 
                              rec( 
                                  content := " \n\nWe say that a digraph is co\
nnected when for every pair of vertices there \nis a path consisting of direct\
ed or reversed edges from one vertex to \nthe other.\n\n", 
                                  count := [ "A", 1, 5, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "G", 
                                              Name := "AutoConnectedComponents\
" ), content := 0, count := [ "A", 1, 6, 2 ], mathmode := "Text", 
                                          name := "Func", next := 59760, 
                                          root := ~, start := 59714, 
                                          stop := 59759 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\nComputes a list\
 of the connected components of the digraph\n\n", count := [ "A", 1, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> G:\
=RandomDiGraph(6);\n[ [  ], [ 1, 4, 5, 6 ], [  ], [ 1, 3, 5, 6 ], [ 2, 3 ], [ \
2, 4, 6 ] ]\ngap> AutoConnectedComponents(G);\n[ [ 1, 2, 3, 4, 5, 6 ] ]\n", 
                                                          count := 
                                                            [ "A", 1, 6, 4 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 6, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 60021, root := ~, 
                                                  start := 59835, 
                                                  stop := 60020 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 6, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "A", 1, 6, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 60036, root := ~, 
                                          start := 59761, stop := 60035 ) ], 
                                  count := [ "A", 1, 6, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 60052, root := ~, start := 59700, 
                                  stop := 60051 ), 
                              rec( 
                                  content := " \n\nTwo vertices of a digraph b\
elong to a strongly connected component if there is a directed path from each \
one to the other.", count := [ "A", 1, 6, 5 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ "A", 1, 6, 6 ], 
                                  mathmode := "Text", name := "P", 
                                  next := 60181, root := ~, start := 60177, 
                                  stop := 60180 ), 
                              rec( content := "\n\n", 
                                  count := [ "A", 1, 6, 6 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "G", 
                                              Name := "GraphStronglyConnectedC\
omponents" ), content := 0, count := [ "A", 1, 7, 2 ], mathmode := "Text", 
                                          name := "Func", next := 60252, 
                                          root := ~, start := 60197, 
                                          stop := 60251 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\nProduces the st\
rongly connected components of the digraph ", count := [ "A", 1, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "G", 
                                                          count := 
                                                            [ "A", 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 60333, 
                                                  root := ~, start := 60325, 
                                                  stop := 60332 ), 
                                              rec( content := ". \n", 
                                                  count := [ "A", 1, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> G:\
=RandomDiGraph(6);\n[ [  ], [ 4 ], [  ], [ 4, 6 ], [  ], [ 1, 4, 5, 6 ] ]\ngap\
> GraphStronglyConnectedComponents(G);\n[ [ 1 ], [ 2 ], [ 3 ], [ 4, 6 ], [ 5 ]\
 ]\n", count := [ "A", 1, 7, 4 ], name := "PCDATA", root := ~ ) ], 
                                                  count := [ "A", 1, 7, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 60531, root := ~, 
                                                  start := 60336, 
                                                  stop := 60530 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 7, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "A", 1, 7, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 60546, root := ~, 
                                          start := 60253, stop := 60545 ) ], 
                                  count := [ "A", 1, 7, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 60561, root := ~, start := 60183, 
                                  stop := 60560 ), 
                              rec( content := " \n\n", 
                                  count := [ "A", 1, 7, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "A ", 
                                              Name := "UnderlyingMultiGraphOfA\
utomaton" ), content := 0, count := [ "A", 1, 8, 2 ], mathmode := "Text", 
                                          name := "Func", next := 60633, 
                                          root := ~, start := 60578, 
                                          stop := 60632 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "A", 
                                                          count := 
                                                            [ "A", 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 60656, 
                                                  root := ~, start := 60648, 
                                                  stop := 60655 ), 
                                              rec( 
                                                  content := " is an automaton\
. The output is the underlying directed multi-graph.\n", 
                                                  count := [ "A", 1, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> a:\
=RandomAutomaton(\"det\",3,2);;Display(a);\n   |  1  2  3\n--------------\n a \
|  1  3\n b |     2  3\nInitial state:    [ 1 ]\nAccepting states: [ 1, 2 ]\ng\
ap> UnderlyingMultiGraphOfAutomaton(a);\n[ [ 1 ], [ 3, 2 ], [ 3 ] ]\n", 
                                                          count := 
                                                            [ "A", 1, 8, 4 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 8, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 60978, root := ~, 
                                                  start := 60725, 
                                                  stop := 60977 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 8, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "A", 1, 8, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 60993, root := ~, 
                                          start := 60634, stop := 60992 ) ], 
                                  count := [ "A", 1, 8, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 61008, root := ~, start := 60564, 
                                  stop := 61007 ), 
                              rec( content := " \n\n", 
                                  count := [ "A", 1, 8, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "A", 
                                              Name := "UnderlyingGraphOfAutoma\
ton" ), content := 0, count := [ "A", 1, 9, 2 ], mathmode := "Text", 
                                          name := "Func", next := 61074, 
                                          root := ~, start := 61025, 
                                          stop := 61073 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 9, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "A", 
                                                          count := 
                                                            [ "A", 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 9, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 61097, 
                                                  root := ~, start := 61089, 
                                                  stop := 61096 ), 
                                              rec( 
                                                  content := " is an automaton\
. The output is the underlying directed graph.\n", count := [ "A", 1, 9, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> a:\
=RandomAutomaton(\"det\",3,2);;Display(a);\n   |  1  2  3\n--------------\n a \
|     1  2\n b |  1  2\nInitial state:   [ 2 ]\nAccepting state: [ 2 ]\ngap> U\
nderlyingGraphOfAutomaton(a);\n[ [ 1 ], [ 1, 2 ], [ 2 ] ]\n", 
                                                          count := 
                                                            [ "A", 1, 9, 4 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 9, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 61403, root := ~, 
                                                  start := 61160, 
                                                  stop := 61402 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 9, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "A", 1, 9, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 61418, root := ~, 
                                          start := 61075, stop := 61417 ) ], 
                                  count := [ "A", 1, 9, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 61433, root := ~, start := 61011, 
                                  stop := 61432 ), 
                              rec( content := " \n\n", 
                                  count := [ "A", 1, 9, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "D", 
                                              Name := "DiGraphToRelation" ), 
                                          content := 0, 
                                          count := [ "A", 1, 10, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 61490, root := ~, 
                                          start := 61450, stop := 61489 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\nReturns the rel\
ation corresponding to the digraph. Note that a directed graph may be seen in \
a natural way as a binary relation on the set of vertices.\n", 
                                                  count := [ "A", 1, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> G:\
=RandomDiGraph(4);\n[ [  ], [  ], [ 4 ], [ 4 ] ]\ngap> DiGraphToRelation(G);\n\
[ [ 3, 4 ], [ 4, 4 ] ]\n", count := [ "A", 1, 10, 4 ], name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 10, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 61794, root := ~, 
                                                  start := 61657, 
                                                  stop := 61793 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 10, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "A", 1, 10, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 61809, root := ~, 
                                          start := 61491, stop := 61808 ) ], 
                                  count := [ "A", 1, 10, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 61824, root := ~, start := 61436, 
                                  stop := 61823 ), 
                              rec( content := " \n\n", 
                                  count := [ "A", 1, 10, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "A", 
                                              Name := "MSccAutomaton" ), 
                                          content := 0, 
                                          count := [ "A", 1, 11, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 61877, root := ~, 
                                          start := 61841, stop := 61876 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\nProduces an aut\
omaton where, in each strongly connected component,\nedges labeled by inverses\
 are added. (M stands for modified.)\n", count := [ "A", 1, 11, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 0, 
                                                  count := [ "A", 1, 11, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "P", next := 62025, 
                                                  root := ~, start := 62021, 
                                                  stop := 62024 ), 
                                              rec( 
                                                  content := "\nThis construct\
ion is useful in Finite Semigroup Theory.\n", count := [ "A", 1, 11, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> a:\
=RandomAutomaton(\"det\",3,2);;Display(a);\n   |  1  2  3\n--------------\n a \
|  1  3\n b |  2  3\nInitial state:    [ 1 ]\nAccepting states: [ 1, 2, 3 ]\ng\
ap> MSccAutomaton(a);\n< deterministic automaton on 4 letters with 3 states >\
\ngap> Display(last);\n   |  1  2  3\n--------------\n a |  1  3\n b |  2  3\n\
 A |  1\n B |\nInitial state:    [ 1 ]\nAccepting states: [ 1, 2, 3 ]\n", 
                                                          count := 
                                                            [ "A", 1, 11, 5 ],
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 11, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 62483, root := ~, 
                                                  start := 62082, 
                                                  stop := 62482 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 11, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "A", 1, 11, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 62498, root := ~, 
                                          start := 61878, stop := 62497 ) ], 
                                  count := [ "A", 1, 11, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 62513, root := ~, start := 61827, 
                                  stop := 62512 ), 
                              rec( content := " \n\n\n", 
                                  count := [ "A", 1, 11, 6 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "G", 
                                              Name := "AutoIsAcyclicGraph" ), 
                                          content := 0, 
                                          count := [ "A", 1, 12, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 62572, root := ~, 
                                          start := 62531, stop := 62571 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\nThe argument is\
 a graph's list of adjacencies\nand this function returns true if the argument\
\nis an acyclic graph and false otherwise.\n", count := [ "A", 1, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> Ra\
ndomDiGraph(3);\n[ [  ], [ 3 ], [ 2 ] ]\ngap> AutoIsAcyclicGraph(last);\nfalse\
\n", count := [ "A", 1, 12, 4 ], name := "PCDATA", root := ~ ) ], 
                                                  count := [ "A", 1, 12, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 62836, root := ~, 
                                                  start := 62721, 
                                                  stop := 62835 ), 
                                              rec( content := "\n", 
                                                  count := [ "A", 1, 12, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "A", 1, 12, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 62851, root := ~, 
                                          start := 62573, stop := 62850 ) ], 
                                  count := [ "A", 1, 12, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 62866, root := ~, start := 62517, 
                                  stop := 62865 ), 
                              rec( content := " \n\n\n", 
                                  count := [ "A", 1, 12, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "A", 1, 0, 1 ], 
                          mathmode := "Text", name := "Section", 
                          next := 62880, root := ~, start := 57351, 
                          stop := 62879 ), 
                      rec( content := "\n", count := [ "A", 1, 12, 5 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ) ],
                  count := [ "A", 0, 0, 1 ], mathmode := "Text", 
                  name := "Appendix", next := 62892, root := ~, 
                  start := 57043, stop := 62891 ), 
              rec( content := "xml version=\"1.0\" encoding=\"UTF-8\"", 
                  count := [ "A", 1, 12, 5 ], mathmode := "Text", 
                  name := "XMLPI", root := ~ ), 
              rec( content := " $Id: drawing.xml,v 1.13  Exp $ ", 
                  count := [ "A", 1, 12, 5 ], mathmode := "Text", 
                  name := "XMLCOMMENT", root := ~ ), 
              rec( attributes := rec(  ), 
                  content := 
                    [ 
                      rec( content := "\n    ", count := [ "B", 0, 0, 1 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "\n      Drawing automata\n    ",
                                  count := [ "B", 0, 0, 2 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "B", 0, 0, 2 ], 
                          mathmode := "Text", name := "Heading", 
                          next := 63040, root := ~, start := 62993, 
                          stop := 63039 ), 
                      rec( 
                          content := "\n    The drawing of graphs described he\
re uses\n    ", count := [ "B", 0, 0, 3 ], mathmode := "Text", 
                          name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "graphviz", 
                                  count := [ "B", 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "B", 0, 0, 3 ], 
                          mathmode := "Text", name := "C", next := 63106, 
                          root := ~, start := 63091, stop := 63105 ), 
                      rec( content := " ", count := [ "B", 0, 0, 3 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec( Key := "KoutsofiosNorth:2002" ),
                          content := 0, count := [ "B", 0, 0, 3 ], 
                          mathmode := "Text", name := "Cite", next := 63141, 
                          root := ~, start := 63107, stop := 63140 ), 
                      rec( 
                          content := ", a software for drawing graphs develope\
d at AT\n    ", count := [ "B", 0, 0, 3 ], mathmode := "Text", 
                          name := "PCDATA", root := ~ ), 
                      rec( attributes := rec( Only := "LaTeX" ), 
                          content := 
                            [ 
                              rec( content := "\n      \\&\n    ", 
                                  count := [ "B", 0, 0, 3 ], name := "PCDATA",
                                  root := ~ ) ], count := [ "B", 0, 0, 3 ], 
                          mathmode := "Text", name := "Alt", next := 63235, 
                          root := ~, start := 63193, stop := 63234 ), 
                      rec( content := "\n    ", count := [ "B", 0, 0, 3 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec( Not := "LaTeX" ), 
                          content := 
                            [ 
                              rec( content := "\n      ", 
                                  count := [ "B", 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Only := "HTML" ), 
                                  content := 
                                    [ 
                                      rec( HTML := true, 
                                          content := "\n        &amp;\n      "
                                            , count := [ "B", 0, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "B", 0, 0, 3 ], name := "Alt", 
                                  next := 63312, root := ~, start := 63264, 
                                  stop := 63311 ), 
                              rec( content := "\n      ", 
                                  count := [ "B", 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Not := "HTML" ), 
                                  content := 
                                    [ 
                                      rec( content := "\n        &\n      ", 
                                          count := [ "B", 0, 0, 3 ], 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "B", 0, 0, 3 ], 
                                  mathmode := "Text", name := "Alt", 
                                  next := 63362, root := ~, start := 63319, 
                                  stop := 63361 ), 
                              rec( content := "\n    ", 
                                  count := [ "B", 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "B", 0, 0, 3 ], 
                          name := "Alt", next := 63373, root := ~, 
                          start := 63240, stop := 63372 ), 
                      rec( 
                          content := "\n    T Labs, that can be obtained at\n \
   ", count := [ "B", 0, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                          root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "http://www.graphviz.org/", 
                                  count := [ "B", 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "B", 0, 0, 3 ], 
                          mathmode := "Text", name := "URL", next := 63449, 
                          root := ~, start := 63414, stop := 63448 ), 
                      rec( content := ".\n    ", count := [ "B", 0, 0, 3 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "\n      ", 
                                  count := [ "B", 1, 0, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "\n        Installing some\
 external programs\n      ", count := [ "B", 1, 0, 2 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "B", 1, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 63539, root := ~, start := 63471, 
                                  stop := 63538 ), 
                              rec( 
                                  content := "\n      In order to create the d\
rawings you should install ", count := [ "B", 1, 0, 3 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec( Text := "graphviz" ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "http://www.graphviz.org/"
                                            , count := [ "B", 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "B", 1, 0, 3 ], 
                                  mathmode := "Text", name := "URL", 
                                  next := 63648, root := ~, start := 63597, 
                                  stop := 63647 ), 
                              rec( 
                                  content := "\n      and to view them you sho\
uld install one of ", count := [ "B", 1, 0, 3 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec( Text := "evince" ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "http://www.gnome.org/proj\
ects/evince/", count := [ "B", 1, 0, 3 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "B", 1, 0, 3 ], 
                                  mathmode := "Text", name := "URL", 
                                  next := 63760, root := ~, start := 63698, 
                                  stop := 63759 ), 
                              rec( content := ",\n      ", 
                                  count := [ "B", 1, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Text := "ggv" ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "http://directory.fsf.org/\
GNU/ggv.html", count := [ "B", 1, 0, 3 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "B", 1, 0, 3 ], 
                                  mathmode := "Text", name := "URL", 
                                  next := 63827, root := ~, start := 63768, 
                                  stop := 63826 ), 
                              rec( content := ",\n      ", 
                                  count := [ "B", 1, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Text := "gsview" ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "http://pages.cs.wisc.edu/\
~ghost/gsview/", count := [ "B", 1, 0, 3 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "B", 1, 0, 3 ], 
                                  mathmode := "Text", name := "URL", 
                                  next := 63899, root := ~, start := 63835, 
                                  stop := 63898 ), 
                              rec( content := " or\n      ", 
                                  count := [ "B", 1, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Text := "gv" ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "http://www.gnu.org/softwa\
re/gv/", count := [ "B", 1, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ) ], 
                                  count := [ "B", 1, 0, 3 ], 
                                  mathmode := "Text", name := "URL", 
                                  next := 63961, root := ~, start := 63909, 
                                  stop := 63960 ), 
                              rec( content := ".\n    ", 
                                  count := [ "B", 1, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "B", 1, 0, 1 ], 
                          mathmode := "Text", name := "Section", 
                          next := 63977, root := ~, start := 63455, 
                          stop := 63976 ), 
                      rec( content := "\n    ", count := [ "B", 1, 0, 3 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "\n      ", 
                                  count := [ "B", 2, 0, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "\n        Functions to dr\
aw automata\n      ", count := [ "B", 2, 0, 2 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "B", 2, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 64059, root := ~, start := 63998, 
                                  stop := 64058 ), 
                              rec( content := "\n      ", 
                                  count := [ "B", 2, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( 
                                              Arg := "A [,state_names, L, file\
]", Name := "DrawAutomaton" ), content := 0, count := [ "B", 2, 1, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 64148, root := ~, 
                                          start := 64087, stop := 64147 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n          This \
function draws automaton\n          ", count := [ "B", 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "A", 
                                                          count := 
                                                            [ "B", 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 64229, 
                                                  root := ~, start := 64221, 
                                                  stop := 64228 ), 
                                              rec( 
                                                  content := ".\n\t  The argum\
ents ", count := [ "B", 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "state_nam\
es", count := [ "B", 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 64266, 
                                                  root := ~, start := 64248, 
                                                  stop := 64265 ), 
                                              rec( content := ", ", 
                                                  count := [ "B", 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "L", 
                                                          count := 
                                                            [ "B", 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 64276, 
                                                  root := ~, start := 64268, 
                                                  stop := 64275 ), 
                                              rec( content := " and ", 
                                                  count := [ "B", 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "file", 
                                                          count := 
                                                            [ "B", 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 64292, 
                                                  root := ~, start := 64281, 
                                                  stop := 64291 ), 
                                              rec( 
                                                  content := " are optional.\n\
\n\t  ", count := [ "B", 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 0, 
                                                  count := [ "B", 2, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "P", next := 64316, 
                                                  root := ~, start := 64311, 
                                                  stop := 64315 ), 
                                              rec( 
                                                  content := "\n\t  An automat\
on with ", count := [ "B", 2, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "n", 
                                                          count := 
                                                            [ "B", 2, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 64346, 
                                                  root := ~, start := 64338, 
                                                  stop := 64345 ), 
                                              rec( 
                                                  content := " states will be \
drawn with numbers ", count := [ "B", 2, 1, 4 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "1", 
                                                          count := 
                                                            [ "B", 2, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 64389, 
                                                  root := ~, start := 64381, 
                                                  stop := 64388 ), 
                                              rec( content := " to ", 
                                                  count := [ "B", 2, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "n", 
                                                          count := 
                                                            [ "B", 2, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 64401, 
                                                  root := ~, start := 64393, 
                                                  stop := 64400 ), 
                                              rec( 
                                                  content := "\n\t  written in\
side the corresponding graph node.\n\t  The argument ", 
                                                  count := [ "B", 2, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "state_nam\
es", count := [ "B", 2, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 64484, 
                                                  root := ~, start := 64466, 
                                                  stop := 64483 ), 
                                              rec( 
                                                  content := " is a list of ",
                                                  count := [ "B", 2, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "n", 
                                                          count := 
                                                            [ "B", 2, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 64506, 
                                                  root := ~, start := 64498, 
                                                  stop := 64505 ), 
                                              rec( 
                                                  content := " strings which w\
ill be the new text\n\t  written inside the corresponding graph node.\n\n\t  "
                                                    , 
                                                  count := [ "B", 2, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 0, 
                                                  count := [ "B", 2, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "P", next := 64599, 
                                                  root := ~, start := 64594, 
                                                  stop := 64598 ), 
                                              rec( 
                                                  content := "\n\t  The argume\
nt ", count := [ "B", 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "L", 
                                                          count := 
                                                            [ "B", 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 64624, 
                                                  root := ~, start := 64616, 
                                                  stop := 64623 ), 
                                              rec( 
                                                  content := " is a list of li\
sts of integers, each of which specifies a set\n\t  of states to be drawn in a\
 different color.\n\n\t  ", count := [ "B", 2, 1, 5 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 0, 
                                                  count := [ "B", 2, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "P", next := 64743, 
                                                  root := ~, start := 64738, 
                                                  stop := 64742 ), 
                                              rec( 
                                                  content := "\n\t  The argume\
nt ", count := [ "B", 2, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "file", 
                                                          count := 
                                                            [ "B", 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 64771, 
                                                  root := ~, start := 64760, 
                                                  stop := 64770 ), 
                                              rec( 
                                                  content := " is a string tha\
t specifies the name of the file containing the drawing.\n\t  If it is not giv\
e, it defaults to ", count := [ "B", 2, 1, 6 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\"automat\
on\"", count := [ "B", 2, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 64899, 
                                                  root := ~, start := 64881, 
                                                  stop := 64898 ), 
                                              rec( content := ".\n", 
                                                  count := [ "B", 2, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> x:\
=Automaton(\"det\",3,2,[ [ 2, 3, 0 ], [ 0, 1, 2 ] ],[ 1 ],[ 1, 2, 3 ]);;\ngap>\
 DrawAutomaton(x,\"file_name\");\nDisplaying file: /tmp/tmp.Rj0v1s/file_name.d\
ot.ps\n\ngap> DrawAutomaton(x,[\"st 1\", \"2\", \"C\"],\"file_name\");\nDispla\
ying file: /tmp/tmp.BCH3FO/file_name.dot.ps\n\ngap> DrawAutomaton(x,[\"st 1\",\
 \"2\", \"C\"],[[2],[1,3]]);\nDisplaying file: /tmp/tmp.LPnJMq/automaton.dot.p\
s\n", count := [ "B", 2, 1, 7 ], name := "PCDATA", root := ~ ) ], 
                                                  count := [ "B", 2, 1, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 65306, root := ~, 
                                                  start := 64901, 
                                                  stop := 65305 ), 
                                              rec( 
                                                  content := "\nThe output of \
the three previous ", count := [ "B", 2, 1, 8 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "DrawAutom\
aton", count := [ "B", 2, 1, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 8 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 65360, 
                                                  root := ~, start := 65340, 
                                                  stop := 65359 ), 
                                              rec( 
                                                  content := " commands would \
be the following diagrams displayed in a ", count := [ "B", 2, 1, 8 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "ghostview\
", count := [ "B", 2, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ "B", 2, 1, 8 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 65433, 
                                                  root := ~, start := 65417, 
                                                  stop := 65432 ), 
                                              rec( 
                                                  content := " window,\nrespec\
tively.\n", count := [ "B", 2, 1, 8 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 0, 
                                                  count := [ "B", 2, 1, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "P", next := 65461, 
                                                  root := ~, start := 65456, 
                                                  stop := 65460 ), 
                                              rec( content := "\n    ", 
                                                  count := [ "B", 2, 1, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Only := "LaTeX" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      \\
\begin{figure}[htbp] \\begin{center} \\leavevmode \\includegraphics[bb=0 0 74 \
250]{aut2.jpg} \\end{center} \\label{fig:aut2} \\end{figure}\n    ", 
                                                          count := 
                                                            [ "B", 2, 1, 9 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Alt", 
                                                  next := 65634, root := ~, 
                                                  start := 65466, 
                                                  stop := 65633 ), 
                                              rec( content := "\n    ", 
                                                  count := [ "B", 2, 1, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Only := "HTML" ), 
                                                  content := 
                                                    [ 
                                                      rec( HTML := true, 
                                                          content := "\n      \
<br><center><img src=\"aut2.jpg\"></center><br>\n    ", count := 
                                                            [ "B", 2, 1, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 9 ], 
                                                  name := "Alt", 
                                                  next := 65767, root := ~, 
                                                  start := 65639, 
                                                  stop := 65766 ), 
                                              rec( content := "\n    ", 
                                                  count := [ "B", 2, 1, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 0, 
                                                  count := [ "B", 2, 1, 10 ], 
                                                  mathmode := "Text", 
                                                  name := "P", next := 65777, 
                                                  root := ~, start := 65772, 
                                                  stop := 65776 ), 
                                              rec( content := "\n    ", 
                                                  count := [ "B", 2, 1, 10 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Only := "LaTeX" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      \\
\begin{figure}[htbp] \\begin{center} \\leavevmode \\includegraphics[bb=0 0 100\
 250]{aut2_1.jpg} \\end{center} \\label{fig:aut2_1} \\end{figure}\n    ", 
                                                          count := 
                                                            [ "B", 2, 1, 10 ],
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 10 ], 
                                                  mathmode := "Text", 
                                                  name := "Alt", 
                                                  next := 65955, root := ~, 
                                                  start := 65782, 
                                                  stop := 65954 ), 
                                              rec( content := "\n    ", 
                                                  count := [ "B", 2, 1, 10 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Only := "HTML" ), 
                                                  content := 
                                                    [ 
                                                      rec( HTML := true, 
                                                          content := "\n      \
<br><center><img src=\"aut2_1.jpg\"></center><br>\n    ", count := 
                                                            [ "B", 2, 1, 10 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 10 ], 
                                                  name := "Alt", 
                                                  next := 66090, root := ~, 
                                                  start := 65960, 
                                                  stop := 66089 ), 
                                              rec( content := "\n    ", 
                                                  count := [ "B", 2, 1, 10 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 0, 
                                                  count := [ "B", 2, 1, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "P", next := 66100, 
                                                  root := ~, start := 66095, 
                                                  stop := 66099 ), 
                                              rec( content := "\n    ", 
                                                  count := [ "B", 2, 1, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Only := "LaTeX" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      \\
\begin{figure}[htbp] \\begin{center} \\leavevmode \\includegraphics[bb=0 0 100\
 250]{aut2_2.jpg} \\end{center} \\label{fig:aut2_2} \\end{figure}\n    ", 
                                                          count := 
                                                            [ "B", 2, 1, 11 ],
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "Alt", 
                                                  next := 66278, root := ~, 
                                                  start := 66105, 
                                                  stop := 66277 ), 
                                              rec( content := "\n    ", 
                                                  count := [ "B", 2, 1, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Only := "HTML" ), 
                                                  content := 
                                                    [ 
                                                      rec( HTML := true, 
                                                          content := "\n      \
<br><center><img src=\"aut2_2.jpg\"></center><br>\n    ", count := 
                                                            [ "B", 2, 1, 11 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 1, 11 ], 
                                                  name := "Alt", 
                                                  next := 66413, root := ~, 
                                                  start := 66283, 
                                                  stop := 66412 ), 
                                              rec( content := "\n    ", 
                                                  count := [ "B", 2, 1, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 0, 
                                                  count := [ "B", 2, 1, 12 ], 
                                                  mathmode := "Text", 
                                                  name := "P", next := 66423, 
                                                  root := ~, start := 66418, 
                                                  stop := 66422 ), 
                                              rec( content := "\n        ", 
                                                  count := [ "B", 2, 1, 12 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "B", 2, 1, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 66446, root := ~, 
                                          start := 64157, stop := 66445 ) ], 
                                  count := [ "B", 2, 1, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 66466, root := ~, start := 64066, 
                                  stop := 66465 ), 
                              rec( content := "\n      ", 
                                  count := [ "B", 2, 1, 12 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "A, B [, file]", 
                                              Name := "DrawAutomata" ), 
                                          content := 0, 
                                          count := [ "B", 2, 2, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 66542, root := ~, 
                                          start := 66494, stop := 66541 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n          This \
function tests if automaton\n          ", count := [ "B", 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
     A\n          ", count := [ "B", 2, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 66650, 
                                                  root := ~, start := 66618, 
                                                  stop := 66649 ), 
                                              rec( 
                                                  content := "\n          is a\
 subautomaton of\n          ", count := [ "B", 2, 2, 3 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
     B\n          ", count := [ "B", 2, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 66724, 
                                                  root := ~, start := 66692, 
                                                  stop := 66723 ), 
                                              rec( 
                                                  content := "\n          in w\
hich case draws\n          ", count := [ "B", 2, 2, 3 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
     B\n          ", count := [ "B", 2, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 66797, 
                                                  root := ~, start := 66765, 
                                                  stop := 66796 ), 
                                              rec( 
                                                  content := "\n          high\
lighting the edges not in\n          ", count := [ "B", 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
     A\n          ", count := [ "B", 2, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 66880, 
                                                  root := ~, start := 66848, 
                                                  stop := 66879 ), 
                                              rec( 
                                                  content := "\n          by d\
rawing them in a dotted style, while the others are drawn in a plain style.\n \
       ", count := [ "B", 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ "B", 2, 2, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 66993, root := ~, 
                                          start := 66551, stop := 66992 ) ], 
                                  count := [ "B", 2, 2, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 67013, root := ~, start := 66473, 
                                  stop := 67012 ), 
                              rec( content := "\n      ", 
                                  count := [ "B", 2, 2, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "G [, file]", 
                                              Name := "DrawGraph" ), 
                                          content := 0, 
                                          count := [ "B", 2, 3, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 67083, root := ~, 
                                          start := 67041, stop := 67082 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n          Draws\
 a graph specified as an adjacency list\n          ", 
                                                  count := [ "B", 2, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "G", 
                                                          count := 
                                                            [ "B", 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 67179, 
                                                  root := ~, start := 67171, 
                                                  stop := 67178 ), 
                                              rec( content := ".\n        ", 
                                                  count := [ "B", 2, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "B", 2, 3, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 67203, root := ~, 
                                          start := 67092, stop := 67202 ) ], 
                                  count := [ "B", 2, 3, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 67223, root := ~, start := 67020, 
                                  stop := 67222 ), 
                              rec( content := "\n      ", 
                                  count := [ "B", 2, 3, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( 
                                              Arg := "A [,state_names, L, file\
]", Name := "DrawSCCAutomaton" ), content := 0, count := [ "B", 2, 4, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 67315, root := ~, 
                                          start := 67251, stop := 67314 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n          Draws\
 automaton\n          ", count := [ "B", 2, 4, 3 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
     A\n          ", count := [ "B", 2, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 67406, 
                                                  root := ~, start := 67374, 
                                                  stop := 67405 ), 
                                              rec( 
                                                  content := "\n          and \
highlights it's strongly connected components by drawing the other edges in a \
dotted style.\n\t  ", count := [ "B", 2, 4, 3 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 0, 
                                                  count := [ "B", 2, 4, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "P", next := 67525, 
                                                  root := ~, start := 67520, 
                                                  stop := 67524 ), 
                                              rec( 
                                                  content := "\n\t  The option\
al arguments ", count := [ "B", 2, 4, 4 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "state_nam\
es", count := [ "B", 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 4, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 67570, 
                                                  root := ~, start := 67552, 
                                                  stop := 67569 ), 
                                              rec( content := ", ", 
                                                  count := [ "B", 2, 4, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "L", 
                                                          count := 
                                                            [ "B", 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 4, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 67580, 
                                                  root := ~, start := 67572, 
                                                  stop := 67579 ), 
                                              rec( content := " and ", 
                                                  count := [ "B", 2, 4, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "file", 
                                                          count := 
                                                            [ "B", 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "B", 2, 4, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 67596, 
                                                  root := ~, start := 67585, 
                                                  stop := 67595 ), 
                                              rec( 
                                                  content := " are as describe\
d in\n\t  ", count := [ "B", 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Func := "DrawAutomaton" 
                                                     ), content := 0, 
                                                  count := [ "B", 2, 4, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Ref", 
                                                  next := 67648, root := ~, 
                                                  start := 67620, 
                                                  stop := 67647 ), 
                                              rec( content := ".\n        ", 
                                                  count := [ "B", 2, 4, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "B", 2, 4, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 67672, root := ~, 
                                          start := 67324, stop := 67671 ) ], 
                                  count := [ "B", 2, 4, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 67692, root := ~, start := 67230, 
                                  stop := 67691 ), 
                              rec( content := "\n    ", 
                                  count := [ "B", 2, 4, 4 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "B", 2, 0, 1 ], 
                          mathmode := "Text", name := "Section", 
                          next := 67707, root := ~, start := 63982, 
                          stop := 67706 ), 
                      rec( content := "\n\n    ", count := [ "B", 2, 4, 4 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "\n       ", 
                                  count := [ "B", 3, 0, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Drawings output formats"
                                            , count := [ "B", 3, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "B", 3, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 67772, root := ~, start := 67730, 
                                  stop := 67771 ), 
                              rec( 
                                  content := "\n       Since drawings are most\
ly used in the ", count := [ "B", 3, 0, 3 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "SgpViz", 
                                          count := [ "B", 3, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "B", 3, 0, 3 ], 
                                  mathmode := "Text", name := "Package", 
                                  next := 67843, root := ~, start := 67818, 
                                  stop := 67842 ), 
                              rec( 
                                  content := " package, please\n       refer t\
o that package's\n       ", count := [ "B", 3, 0, 3 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec( Text := "manual" ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "http://www.gap-system.org\
/Manuals/pkg/sgpviz/doc/manual.html", count := [ "B", 3, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "B", 3, 0, 3 ], 
                                  mathmode := "Text", name := "URL", 
                                  next := 67983, root := ~, start := 67898, 
                                  stop := 67982 ), 
                              rec( 
                                  content := "\n       section of the same nam\
e.\n    ", count := [ "B", 3, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "B", 3, 0, 1 ], 
                          mathmode := "Text", name := "Section", 
                          next := 68031, root := ~, start := 67713, 
                          stop := 68030 ), 
                      rec( content := "\n    \n    ", 
                          count := [ "B", 3, 0, 3 ], mathmode := "Text", 
                          name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "\n            ", 
                                  count := [ "B", 4, 0, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "Drawings extra graph attr\
ibutes", count := [ "B", 4, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ) ], 
                                  count := [ "B", 4, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 68113, root := ~, start := 68063, 
                                  stop := 68112 ), 
                              rec( 
                                  content := "\n       Since drawings are most\
ly used in the ", count := [ "B", 4, 0, 3 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "SgpViz", 
                                          count := [ "B", 4, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "B", 4, 0, 3 ], 
                                  mathmode := "Text", name := "Package", 
                                  next := 68184, root := ~, start := 68159, 
                                  stop := 68183 ), 
                              rec( 
                                  content := " package, please\n       refer t\
o that package's\n       ", count := [ "B", 4, 0, 3 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec( Text := "manual" ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "http://www.gap-system.org\
/Manuals/pkg/sgpviz/doc/manual.html", count := [ "B", 4, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "B", 4, 0, 3 ], 
                                  mathmode := "Text", name := "URL", 
                                  next := 68324, root := ~, start := 68239, 
                                  stop := 68323 ), 
                              rec( 
                                  content := "\n       section of the same nam\
e.\n    ", count := [ "B", 4, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "B", 4, 0, 1 ], 
                          mathmode := "Text", name := "Section", 
                          next := 68372, root := ~, start := 68041, 
                          stop := 68371 ), 
                      rec( content := "\n  ", count := [ "B", 4, 0, 3 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ) ],
                  count := [ "B", 0, 0, 1 ], mathmode := "Text", 
                  name := "Appendix", next := 68386, root := ~, 
                  start := 62978, stop := 68385 ), 
              rec( content := "xml version=\"1.0\" encoding=\"UTF-8\"", 
                  count := [ "B", 4, 0, 3 ], mathmode := "Text", 
                  name := "XMLPI", root := ~ ), 
              rec( content := " $Id: foldings.xml,v 1.13  Exp $ ", 
                  count := [ "B", 4, 0, 3 ], mathmode := "Text", 
                  name := "XMLCOMMENT", root := ~ ), 
              rec( attributes := rec(  ), 
                  content := 
                    [ 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( 
                                  content := "Inverse automata and subgroups of\
 the free group", count := [ "C", 0, 0, 2 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ "C", 0, 0, 2 ], mathmode := "Text", 
                          name := "Heading", next := 68546, root := ~, 
                          start := 68479, stop := 68545 ), 
                      rec( 
                          content := "\n\nInverse automata with a single initi\
al/accepting state are in a one to one correspondence with finitely generated \
subgroups of the free group over the alphabet of the automaton. See  ", 
                          count := [ "C", 0, 0, 3 ], mathmode := "Text", 
                          name := "PCDATA", root := ~ ), 
                      rec( attributes := rec( Key := "MSW:2001" ), 
                          content := 0, count := [ "C", 0, 0, 3 ], 
                          mathmode := "Text", name := "Cite", next := 68753, 
                          root := ~, start := 68731, stop := 68752 ), 
                      rec( content := ", ", count := [ "C", 0, 0, 3 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec( Key := "KM:2002" ), 
                          content := 0, count := [ "C", 0, 0, 3 ], 
                          mathmode := "Text", name := "Cite", next := 68777, 
                          root := ~, start := 68755, stop := 68776 ), 
                      rec( 
                          content := " for details, as well as for concepts su\
ch as ", count := [ "C", 0, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                          root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "flower automaton", 
                                  count := [ "C", 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "C", 0, 0, 3 ], 
                          mathmode := "Text", name := "E", next := 68846, 
                          root := ~, start := 68823, stop := 68845 ), 
                      rec( content := " and ", count := [ "C", 0, 0, 3 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Stallings foldings", 
                                  count := [ "C", 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "C", 0, 0, 3 ], 
                          mathmode := "Text", name := "E", next := 68876, 
                          root := ~, start := 68851, stop := 68875 ), 
                      rec( content := ".\n\n\n", count := [ "C", 0, 0, 3 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "From subgroups to inverse\
 automata", count := [ "C", 1, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ) ], 
                                  count := [ "C", 1, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 68942, root := ~, start := 68889, 
                                  stop := 68941 ), 
                              rec( 
                                  content := "\n\nA finitely generated subgrou\
p of a finitely generated free group is given\nthrough a list whose first elem\
ent is the number of generators of the \nfree group and the remaining elements\
 are the generators of the subgroup.\nThe set of generators of the free group \
of rank ", count := [ "C", 1, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "n", 
                                          count := [ "C", 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "C", 1, 0, 3 ], 
                                  mathmode := "Text", name := "M", 
                                  next := 69219, root := ~, start := 69211, 
                                  stop := 69218 ), 
                              rec( content := " consists on the ", 
                                  count := [ "C", 1, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "n", 
                                          count := [ "C", 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "C", 1, 0, 3 ], 
                                  mathmode := "Text", name := "M", 
                                  next := 69244, root := ~, start := 69236, 
                                  stop := 69243 ), 
                              rec( content := " first letters of the set ", 
                                  count := [ "C", 1, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "\\{a,b,c,d,e,f,g\\}", 
                                          count := [ "C", 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "C", 1, 0, 3 ], 
                                  mathmode := "Text", name := "M", 
                                  next := 69294, root := ~, start := 69270, 
                                  stop := 69293 ), 
                              rec( 
                                  content := ". In particular, free groups of \
rank greater than ", count := [ "C", 1, 0, 3 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "8", 
                                          count := [ "C", 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "C", 1, 0, 3 ], 
                                  mathmode := "Text", name := "M", 
                                  next := 69352, root := ~, start := 69344, 
                                  stop := 69351 ), 
                              rec( 
                                  content := " must not be considered. A forma\
l inverse of a generator is represented by the corresponding capital letter.\n\
", count := [ "C", 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                 ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ "C", 1, 0, 4 ], 
                                  mathmode := "Text", name := "P", 
                                  next := 69465, root := ~, start := 69461, 
                                  stop := 69464 ), 
                              rec( 
                                  content := "\nA generator of the subgroup ma\
y be given through a string of letters or \nthrough a list of positive integer\
s as should be clear from the example that follows. \n", 
                                  count := [ "C", 1, 0, 4 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ "C", 1, 0, 5 ], 
                                  mathmode := "Text", name := "P", 
                                  next := 69630, root := ~, start := 69626, 
                                  stop := 69629 ), 
                              rec( content := "\nFor example, ", 
                                  count := [ "C", 1, 0, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "[2,\"abA\",\"bbabAB\"]",
                                          count := [ "C", 1, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "C", 1, 0, 5 ], 
                                  mathmode := "Text", name := "C", 
                                  next := 69669, root := ~, start := 69644, 
                                  stop := 69668 ), 
                              rec( 
                                  content := " stands for the subgroup of the \
free group of rank 2\non the generators ", count := [ "C", 1, 0, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "aba^{-1}", 
                                          count := [ "C", 1, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "C", 1, 0, 5 ], 
                                  mathmode := "Text", name := "M", 
                                  next := 69755, root := ~, start := 69740, 
                                  stop := 69754 ), 
                              rec( content := " and ", 
                                  count := [ "C", 1, 0, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "bbaba^{-1}b^{-1}", 
                                          count := [ "C", 1, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "C", 1, 0, 5 ], 
                                  mathmode := "Text", name := "M", 
                                  next := 69783, root := ~, start := 69760, 
                                  stop := 69782 ), 
                              rec( 
                                  content := ".\nThe same subgroup may be give\
n as ", count := [ "C", 1, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "[2,[1,2,3],[2,2,1,2,3,4]]\
", count := [ "C", 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                         ) ], count := [ "C", 1, 0, 5 ], 
                                  mathmode := "Text", name := "C", 
                                  next := 69851, root := ~, start := 69819, 
                                  stop := 69850 ), 
                              rec( content := ". The number ", 
                                  count := [ "C", 1, 0, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := " n+j", 
                                          count := [ "C", 1, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "C", 1, 0, 5 ], 
                                  mathmode := "Text", name := "M", 
                                  next := 69875, root := ~, start := 69864, 
                                  stop := 69874 ), 
                              rec( 
                                  content := " represents the formal inverse o\
f the generator represented by ", count := [ "C", 1, 0, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "j", 
                                          count := [ "C", 1, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "C", 1, 0, 5 ], 
                                  mathmode := "Text", name := "M", 
                                  next := 69946, root := ~, start := 69938, 
                                  stop := 69945 ), 
                              rec( 
                                  content := ". One can go from one representa\
tion to another, using the following functions.\n\n", 
                                  count := [ "C", 1, 0, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "L", 
                                              Name := "GeneratorsToListReprese\
ntation" ), content := 0, count := [ "C", 1, 1, 2 ], mathmode := "Text", 
                                          name := "Func", next := 70094, 
                                          root := ~, start := 70041, 
                                          stop := 70093 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := " \n", 
                                                  count := [ "C", 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> L:\
=[2,\"abA\",\"bbabAB\"];;\ngap> GeneratorsToListRepresentation(L);\n[ 2, [ 1, \
2, 3 ], [ 2, 2, 1, 2, 3, 4 ] ]\n", count := [ "C", 1, 1, 4 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "C", 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 70252, root := ~, 
                                                  start := 70110, 
                                                  stop := 70251 ), 
                                              rec( content := "\n", 
                                                  count := [ "C", 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "C", 1, 1, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 70267, root := ~, 
                                          start := 70095, stop := 70266 ) ], 
                                  count := [ "C", 1, 1, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 70282, root := ~, start := 70027, 
                                  stop := 70281 ), 
                              rec( content := " \n\n\n", 
                                  count := [ "C", 1, 1, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "K", 
                                              Name := "ListToGeneratorsReprese\
ntation" ), content := 0, count := [ "C", 1, 2, 2 ], mathmode := "Text", 
                                          name := "Func", next := 70353, 
                                          root := ~, start := 70300, 
                                          stop := 70352 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "\n", 
                                                  count := [ "C", 1, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> K:\
=[2,[1,2,3],[2,2,1,2,3,4]];;\ngap> ListToGeneratorsRepresentation(K);\n[ 2, \"\
abA\", \"bbabAB\" ]\n", count := [ "C", 1, 2, 4 ], name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "C", 1, 2, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 70499, root := ~, 
                                                  start := 70368, 
                                                  stop := 70498 ), 
                                              rec( content := "\n", 
                                                  count := [ "C", 1, 2, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "C", 1, 2, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 70514, root := ~, 
                                          start := 70354, stop := 70513 ) ], 
                                  count := [ "C", 1, 2, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 70528, root := ~, start := 70286, 
                                  stop := 70527 ), 
                              rec( content := " \n\n", 
                                  count := [ "C", 1, 2, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "L", 
                                              Name := "FlowerAutomaton" ), 
                                          content := 0, 
                                          count := [ "C", 1, 3, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 70583, root := ~, 
                                          start := 70545, stop := 70582 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\nThe argument ",
                                                  count := [ "C", 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "L", 
                                                          count := 
                                                            [ "C", 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "C", 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 70619, 
                                                  root := ~, start := 70611, 
                                                  stop := 70618 ), 
                                              rec( 
                                                  content := " is a subgroup o\
f the free group given through any \nof the representations described above. R\
eturns the flower automaton.\n", count := [ "C", 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> W:\
=[2,\"bbbAB\",\"abAbA\"];;\ngap> A:=FlowerAutomaton(W);\n< non deterministic a\
utomaton on 2 letters with 9 states >\ngap> Display(A);\n   |  1          2   \
    3       4    5       6       7    8       9\n-----------------------------\
----------------------------------------\n a | [ 6, 9 ]                       \
 [ 4 ]                [ 7 ]\n b | [ 2, 5 ]   [ 3 ]   [ 4 ]                [ 7 \
]        [ 9 ]\nInitial state:   [ 1 ]\nAccepting state: [ 1 ]\n", 
                                                          count := 
                                                            [ "C", 1, 3, 4 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "C", 1, 3, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 71220, root := ~, 
                                                  start := 70741, 
                                                  stop := 71219 ), 
                                              rec( content := "\n", 
                                                  count := [ "C", 1, 3, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "C", 1, 3, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 71235, root := ~, 
                                          start := 70584, stop := 71234 ) ], 
                                  count := [ "C", 1, 3, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 71249, root := ~, start := 70531, 
                                  stop := 71248 ), 
                              rec( content := " \n\n", 
                                  count := [ "C", 1, 3, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "A", 
                                              Name := "FoldFlowerAutomaton" ),
                                          content := 0, 
                                          count := [ "C", 1, 4, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 71308, root := ~, 
                                          start := 71266, stop := 71307 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n Makes identifi\
cations on the flower automaton ", count := [ "C", 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "A", 
                                                          count := 
                                                            [ "C", 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "C", 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 71378, 
                                                  root := ~, start := 71370, 
                                                  stop := 71377 ), 
                                              rec( 
                                                  content := ". In the literat\
ure, these identifications are called Stallings foldings.\n", 
                                                  count := [ "C", 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 0, 
                                                  count := [ "C", 1, 4, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "P", next := 71456, 
                                                  root := ~, start := 71452, 
                                                  stop := 71455 ), 
                                              rec( 
                                                  content := "\n(This function\
 may have ", count := [ "C", 1, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "true", 
                                                          count := 
                                                            [ "C", 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "C", 1, 4, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 71492, 
                                                  root := ~, start := 71481, 
                                                  stop := 71491 ), 
                                              rec( 
                                                  content := " as a second arg\
ument. WARNING: the second argument should only be used when facilities to dra\
w automata are available. In that case, one may visualize the identifications \
that are taking place.)\n", count := [ "C", 1, 4, 4 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> B \
:= FoldFlowerAutomaton(A);\n< deterministic automaton on 2 letters with 7 stat\
es >\ngap> Display(B);\n   |  1  2  3  4  5  6  7\n--------------------------\
\n a |  5  4              6\n b |  2  3  4     6     5\nInitial state:   [ 1 ]\
\nAccepting state: [ 1 ]\n", count := [ "C", 1, 4, 5 ], name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "C", 1, 4, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 71977, root := ~, 
                                                  start := 71688, 
                                                  stop := 71976 ), 
                                              rec( content := "\n", 
                                                  count := [ "C", 1, 4, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "C", 1, 4, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 71992, root := ~, 
                                          start := 71309, stop := 71991 ) ], 
                                  count := [ "C", 1, 4, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 72006, root := ~, start := 71252, 
                                  stop := 72005 ), 
                              rec( content := "\n", count := [ "C", 1, 4, 6 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "L", 
                                              Name := "SubgroupGenToInvAut" ),
                                          content := 0, 
                                          count := [ "C", 1, 5, 2 ], 
                                          mathmode := "Text", name := "Func", 
                                          next := 72063, root := ~, 
                                          start := 72021, stop := 72062 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\nReturns the inv\
erse automaton corresponding to the subgroup given by \n", 
                                                  count := [ "C", 1, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "L", 
                                                          count := 
                                                            [ "C", 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "C", 1, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 72156, 
                                                  root := ~, start := 72148, 
                                                  stop := 72155 ), 
                                              rec( content := ".\n", 
                                                  count := [ "C", 1, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> L:\
=[2,\"bbbAB\",\"AbAbA\"];;\ngap> SubgroupGenToInvAut(L);\n< deterministic auto\
maton on 2 letters with 8 states >\ngap> Display(last);\n   |  1  2  3  4  5  \
6  7  8\n-----------------------------\n a |  8  4        1     6\n b |  2  3 \
 4     6     8\nInitial state:   [ 1 ]\nAccepting state: [ 1 ]\n\n", 
                                                          count := 
                                                            [ "C", 1, 5, 4 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "C", 1, 5, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 72482, root := ~, 
                                                  start := 72158, 
                                                  stop := 72481 ), 
                                              rec( content := "\n", 
                                                  count := [ "C", 1, 5, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "C", 1, 5, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 72497, root := ~, 
                                          start := 72064, stop := 72496 ) ], 
                                  count := [ "C", 1, 5, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 72511, root := ~, start := 72007, 
                                  stop := 72510 ), 
                              rec( content := "\n", count := [ "C", 1, 5, 5 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "C", 1, 0, 1 ], 
                          mathmode := "Text", name := "Section", 
                          next := 72522, root := ~, start := 68880, 
                          stop := 72521 ), 
                      rec( content := "\n", count := [ "C", 1, 5, 5 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "From inverse automata to \
subgroups", count := [ "C", 2, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ) ], 
                                  count := [ "C", 2, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 72585, root := ~, start := 72532, 
                                  stop := 72584 ), 
                              rec( 
                                  content := "\nGiven an inverse automaton wit\
h a single initial/accepting state, one can find a set of generators for the s\
ubgroup represented by the automaton. Moreover, using a geodesic tree, one can\
 find a Nielsen reduced set of generators ", count := [ "C", 2, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Key := "KM:2002" ), 
                                  content := 0, count := [ "C", 2, 0, 3 ], 
                                  mathmode := "Text", name := "Cite", 
                                  next := 72836, root := ~, start := 72814, 
                                  stop := 72835 ), 
                              rec( content := ".\n\n", 
                                  count := [ "C", 2, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "A", 
                                              Name := "GeodesicTreeOfInverseAu\
tomaton" ), content := 0, count := [ "C", 2, 1, 2 ], mathmode := "Text", 
                                          name := "Func", next := 72906, 
                                          root := ~, start := 72853, 
                                          stop := 72905 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\nReturns a subau\
tomaton of ", count := [ "C", 2, 1, 3 ], mathmode := "Text", name := "PCDATA",
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "A", 
                                                          count := 
                                                            [ "C", 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "C", 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "A", next := 72955, 
                                                  root := ~, start := 72947, 
                                                  stop := 72954 ), 
                                              rec( 
                                                  content := "whose underlying\
 graph is a geodesic tree of the underlying graph of the inverse automaton ", 
                                                  count := [ "C", 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "A", 
                                                          count := 
                                                            [ "C", 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "C", 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 73054, 
                                                  root := ~, start := 73046, 
                                                  stop := 73053 ), 
                                              rec( content := ".  \n", 
                                                  count := [ "C", 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> A:\
=Automaton(\"det\",4,2,[ [ 3, 4, 0, 0 ], [ 2, 3, 4, 0 ] ],[ 1 ],[ 1 ]);;\ngap>\
 G := GeodesicTreeOfInverseAutomaton(A);\n< deterministic automaton on 2 lette\
rs with 4 states >\ngap> Display(G);\n   |  1  2  3  4\n-----------------\n a \
|  3\n b |  2     4\nInitial state:   [ 1 ]\nAccepting state: [ 1 ]\n", 
                                                          count := 
                                                            [ "C", 2, 1, 4 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "C", 2, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 73388, root := ~, 
                                                  start := 73058, 
                                                  stop := 73387 ), 
                                              rec( content := "\n", 
                                                  count := [ "C", 2, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "C", 2, 1, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 73403, root := ~, 
                                          start := 72907, stop := 73402 ) ], 
                                  count := [ "C", 2, 1, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 73418, root := ~, start := 72839, 
                                  stop := 73417 ), 
                              rec( content := " \n\n", 
                                  count := [ "C", 2, 1, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          attributes := 
                                            rec( Arg := "A", 
                                              Name := "InverseAutomatonToGener\
ators" ), content := 0, count := [ "C", 2, 2, 2 ], mathmode := "Text", 
                                          name := "Func", next := 73486, 
                                          root := ~, start := 73435, 
                                          stop := 73485 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\nReturns a set o\
f generators (given trough the representation above) of the \nsubgroup of the \
free group corresponding to the automaton ", count := [ "C", 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "A", 
                                                          count := 
                                                            [ "C", 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "C", 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "C", next := 73643, 
                                                  root := ~, start := 73635, 
                                                  stop := 73642 ), 
                                              rec( content := " given.\n", 
                                                  count := [ "C", 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\ngap> NW\
 := InverseAutomatonToGenerators(A);\n[ 2, \"baBA\", \"bbA\" ]\n", 
                                                          count := 
                                                            [ "C", 2, 2, 4 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "C", 2, 2, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Example", 
                                                  next := 73748, root := ~, 
                                                  start := 73651, 
                                                  stop := 73747 ), 
                                              rec( content := "\n", 
                                                  count := [ "C", 2, 2, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ "C", 2, 2, 3 ], 
                                          mathmode := "Text", 
                                          name := "Description", 
                                          next := 73763, root := ~, 
                                          start := 73487, stop := 73762 ) ], 
                                  count := [ "C", 2, 2, 1 ], 
                                  mathmode := "Text", name := "ManSection", 
                                  next := 73778, root := ~, start := 73421, 
                                  stop := 73777 ), 
                              rec( content := " \n\n", 
                                  count := [ "C", 2, 2, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "C", 2, 0, 1 ], 
                          mathmode := "Text", name := "Section", 
                          next := 73791, root := ~, start := 72523, 
                          stop := 73790 ), 
                      rec( content := "\n", count := [ "C", 2, 2, 5 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ) ],
                  count := [ "C", 0, 0, 1 ], mathmode := "Text", 
                  name := "Appendix", next := 73803, root := ~, 
                  start := 68469, stop := 73802 ), 
              rec( attributes := rec( Databases := "AutMan" ), content := 0, 
                  count := [ "Bib", 0, 0, 1 ], mathmode := "Text", 
                  name := "Bibliography", next := 73844, root := ~, 
                  start := 73809, stop := 73843 ), 
              rec( attributes := rec(  ), content := 0, 
                  count := [ "Ind", 0, 0, 1 ], mathmode := "Text", 
                  name := "TheIndex", next := 73857, root := ~, 
                  start := 73846, stop := 73856 ) ], count := [ 0, 0, 0, 1 ], 
          name := "Book", next := 73866, root := ~, start := 129, 
          stop := 73865 ), 
      rec( 
          content := " =======================================================\
============= ", count := [ "Ind", 0, 0, 1 ], name := "XMLCOMMENT", root := ~ 
         ) ], count := [ 0, 0, 0, 1 ], indent := "", 
  indextext := "<code class=\"func\"> MinimalAutomaton</code>  <a href=\"chap5\
_mj.html#X7F7AE088808A5D00\">5.2-3</a><br />\n<code class=\"func\"> StarRatExp\
</code>  <a href=\"chap3_mj.html#X83D8DAE6862C8A96\">3.3-3</a><br />\n<code cl\
ass=\"func\">AccessibleAutomaton</code>  <a href=\"chap5_mj.html#X804A6BC979DA\
6E61\">5.2-5</a><br />\n<code class=\"func\">AccessibleStates</code>  <a href=\
\"chap5_mj.html#X7F484D5A781BB643\">5.2-4</a><br />\n<code class=\"func\">AddI\
nverseEdgesToInverseAutomaton</code>  <a href=\"chap2_mj.html#X7A4CDEFB84B9784\
9\">2.4-5</a><br />\n<code class=\"func\">AlphabetOfAutomaton</code>  <a href=\
\"chap2_mj.html#X7A34B47778B50FFE\">2.2-1</a><br />\n<code class=\"func\">Alph\
abetOfAutomatonAsList</code>  <a href=\"chap2_mj.html#X8044B24B82C59BBF\">2.2-\
2</a><br />\n<code class=\"func\">AlphabetOfRatExp</code>  <a href=\"chap3_mj.\
html#X8773359880149A98\">3.1-6</a><br />\n<code class=\"func\">AlphabetOfRatEx\
pAsList</code>  <a href=\"chap3_mj.html#X84B9922B7C006158\">3.1-7</a><br />\n<\
code class=\"func\">AreDisjointLang</code>  <a href=\"chap4_mj.html#X83F1DE067\
C2D31A5\">4.3-5</a><br />\n<code class=\"func\">AreEqualLang</code>  <a href=\
\"chap4_mj.html#X8346D1B17DBF96E7\">4.3-3</a><br />\n<code class=\"func\">AreE\
quivAut</code>  <a href=\"chap4_mj.html#X8346D1B17DBF96E7\">4.3-3</a><br />\n<\
code class=\"func\">AutoConnectedComponents</code>  <a href=\"chapA_mj.html#X7\
F23780E7A12A79E\">A.1-6</a><br />\n<code class=\"func\">AutoIsAcyclicGraph</co\
de>  <a href=\"chapA_mj.html#X7971EE367B6B7F36\">A.1-12</a><br />\n<code class\
=\"func\">Automaton</code>  <a href=\"chap2_mj.html#X87D8222D7B50731E\">2.1-1<\
/a><br />\n<code class=\"func\">AutomatonAllPairsPaths</code>  <a href=\"chap5\
_mj.html#X8460C44386EE6225\">5.2-7</a><br />\n<code class=\"func\">AutomatonTo\
RatExp </code>  <a href=\"chap4_mj.html#X8751E3927CA4DEA1\">4.1-1</a><br />\n<\
code class=\"func\">AutoVertexDegree</code>  <a href=\"chapA_mj.html#X7FA6FAAE\
7AA8715D\">A.1-4</a><br />\n<code class=\"func\">AutToRatExp</code>  <a href=\
\"chap4_mj.html#X8751E3927CA4DEA1\">4.1-1</a><br />\n<code class=\"func\">Copy\
Automaton</code>  <a href=\"chap2_mj.html#X8225A1B886131707\">2.5-1</a><br />\
\n<code class=\"func\">CopyRatExp</code>  <a href=\"chap3_mj.html#X786A096681C\
AC3CD\">3.1-8</a><br />\n<code class=\"func\">DiGraphToRelation</code>  <a hre\
f=\"chapA_mj.html#X78869D478792B3AD\">A.1-10</a><br />\n<code class=\"func\">D\
rawAutomata</code>  <a href=\"chapB_mj.html#X7AEE146D8391CA3D\">B.2-2</a><br /\
>\n<code class=\"func\">DrawAutomaton</code>  <a href=\"chapB_mj.html#X7BC2FDA\
77FD0237B\">B.2-1</a><br />\n<code class=\"func\">DrawGraph</code>  <a href=\"\
chapB_mj.html#X7D17B77F829F9CCB\">B.2-3</a><br />\n<code class=\"func\">DrawSC\
CAutomaton</code>  <a href=\"chapB_mj.html#X7E478FDD807853CA\">B.2-4</a><br />\
\n<code class=\"func\">EpsilonCompactedAut</code>  <a href=\"chap5_mj.html#X87\
1F807D79CE148C\">5.1-3</a><br />\n<code class=\"func\">EpsilonToNFA</code>  <a\
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\">EpsilonToNFASet</code>  <a href=\"chap5_mj.html#X81DC84E17A170270\">5.1-2</\
a><br />\n<code class=\"func\">FAtoRatExp</code>  <a href=\"chap4_mj.html#X875\
1E3927CA4DEA1\">4.1-1</a><br />\n<code class=\"func\">FinalStatesOfAutomaton</\
code>  <a href=\"chap2_mj.html#X78CDDCC27D085F00\">2.2-6</a><br />\n<code clas\
s=\"func\">FiniteRegularLanguageToListOfWords</code>  <a href=\"chap6_mj.html#\
X7E48CD3E78277FF7\">6.1-2</a><br />\n<code class=\"func\">FlowerAutomaton</cod\
e>  <a href=\"chapC_mj.html#X7EAFF7E879D115C5\">C.1-3</a><br />\n<code class=\
\"func\">FoldFlowerAutomaton</code>  <a href=\"chapC_mj.html#X7F729A4E8784D92E\
\">C.1-4</a><br />\n<code class=\"func\">FuseSymbolsAut</code>  <a href=\"chap\
5_mj.html#X7B61945581FE4AC6\">5.1-6</a><br />\n<code class=\"func\">Generators\
ToListRepresentation</code>  <a href=\"chapC_mj.html#X85358D097C314EB5\">C.1-1\
</a><br />\n<code class=\"func\">GeodesicTreeOfInverseAutomaton</code>  <a hre\
f=\"chapC_mj.html#X81DA149779A167BD\">C.2-1</a><br />\n<code class=\"func\">Gr\
aphStronglyConnectedComponents</code>  <a href=\"chapA_mj.html#X7D5288C982F924\
81\">A.1-7</a><br />\n<code class=\"func\">InitialStatesOfAutomaton</code>  <a\
 href=\"chap2_mj.html#X7B5C3CFA83FF80EA\">2.2-4</a><br />\n<code class=\"func\
\">IntersectionAutomaton</code>  <a href=\"chap5_mj.html#X7BAACCAF7E2D213B\">5\
.2-6</a><br />\n<code class=\"func\">IntersectionLanguage</code>  <a href=\"ch\
ap5_mj.html#X7BAACCAF7E2D213B\">5.2-6</a><br />\n<code class=\"func\">InverseA\
utomatonToGenerators</code>  <a href=\"chapC_mj.html#X7F117C43814F2CDE\">C.2-2\
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83CCDEF9814F1E6D\">2.1-2</a><br />\n<code class=\"func\">IsContainedLang</code\
>  <a href=\"chap4_mj.html#X7FCB176285FA5BBB\">4.3-4</a><br />\n<code class=\"\
func\">IsDenseAutomaton</code>  <a href=\"chap2_mj.html#X8356E41086482483\">2.\
4-1</a><br />\n<code class=\"func\">IsDeterministicAutomaton</code>  <a href=\
\"chap2_mj.html#X7D39CECC7E12DD8A\">2.1-3</a><br />\n<code class=\"func\">IsEm\
ptyLang</code>  <a href=\"chap4_mj.html#X84E0143A860889A6\">4.3-1</a><br />\n<\
code class=\"func\">IsEpsilonAutomaton</code>  <a href=\"chap2_mj.html#X81EC53\
31790D6022\">2.1-5</a><br />\n<code class=\"func\">IsFiniteRegularLanguage</co\
de>  <a href=\"chap6_mj.html#X82971FC2851B7B30\">6.1-1</a><br />\n<code class=\
\"func\">IsFullLang</code>  <a href=\"chap4_mj.html#X86AA1A5F7E1EEAFE\">4.3-2<\
/a><br />\n<code class=\"func\">IsInverseAutomaton</code>  <a href=\"chap2_mj.\
html#X7B7CA23680888C9C\">2.4-4</a><br />\n<code class=\"func\">IsNonDeterminis\
ticAutomaton</code>  <a href=\"chap2_mj.html#X83C1148481BAA3DD\">2.1-4</a><br \
/>\n<code class=\"func\">IsPermutationAutomaton</code>  <a href=\"chap2_mj.htm\
l#X80CCDD438258CD25\">2.4-3</a><br />\n<code class=\"func\">IsRationalExpressi\
on</code>  <a href=\"chap3_mj.html#X7DDB46817D6E79BE\">3.1-5</a><br />\n<code \
class=\"func\">IsRecognizedByAutomaton</code>  <a href=\"chap2_mj.html#X8676D8\
388053F1E7\">2.4-2</a><br />\n<code class=\"func\">IsReversibleAutomaton</code\
>  <a href=\"chap2_mj.html#X8321BCE57E55FB30\">2.4-6</a><br />\n<code class=\"\
func\">ListOfWordsToAutomaton</code>  <a href=\"chap6_mj.html#X7F9C5C6F815773E\
6\">6.1-3</a><br />\n<code class=\"func\">ListPermutedAutomata</code>  <a href\
=\"chap2_mj.html#X7A72DDF0782E8D5E\">2.5-7</a><br />\n<code class=\"func\">Lis\
tSinkStatesAut</code>  <a href=\"chap2_mj.html#X79F052EC81135807\">2.5-3</a><b\
r />\n<code class=\"func\">ListToGeneratorsRepresentation</code>  <a href=\"ch\
apC_mj.html#X80F3E10784590374\">C.1-2</a><br />\n<code class=\"func\">Minimali\
zedAut</code>  <a href=\"chap5_mj.html#X83C26846866AEE46\">5.2-2</a><br />\n<c\
ode class=\"func\">MSccAutomaton</code>  <a href=\"chapA_mj.html#X7D63604A8413\
AAAF\">A.1-11</a><br />\n<code class=\"func\">NFAtoDFA</code>  <a href=\"chap5\
_mj.html#X87D0F9F17F2BEB57\">5.1-5</a><br />\n<code class=\"func\">NormalizedA\
utomaton</code>  <a href=\"chap2_mj.html#X7FA7DF6D87D63D67\">2.5-8</a><br />\n\
<code class=\"func\">NullCompletionAutomaton</code>  <a href=\"chap2_mj.html#X\
80D423A584246E2E\">2.5-2</a><br />\n<code class=\"func\">NumberStatesOfAutomat\
on</code>  <a href=\"chap2_mj.html#X7D22AD207A3D5FF4\">2.2-8</a><br />\n<code \
class=\"func\">PermutedAutomaton</code>  <a href=\"chap2_mj.html#X7A4A066583C7\
1ABE\">2.5-6</a><br />\n<code class=\"func\">ProductAutomaton</code>  <a href=\
\"chap2_mj.html#X83E772F2878546A4\">2.5-10</a><br />\n<code class=\"func\">Pro\
ductOfLanguages</code>  <a href=\"chap2_mj.html#X85F6AD697DCA5765\">2.5-11</a>\
<br />\n<code class=\"func\">ProductRatExp</code>  <a href=\"chap3_mj.html#X7E\
29107587611CE2\">3.3-2</a><br />\n<code class=\"func\">RandomAutomaton</code> \
 <a href=\"chap2_mj.html#X801019097C93BCCC\">2.1-7</a><br />\n<code class=\"fu\
nc\">RandomDiGraph</code>  <a href=\"chapA_mj.html#X86CF9F66788B2A24\">A.1-1</\
a><br />\n<code class=\"func\">RandomRatExp</code>  <a href=\"chap3_mj.html#X7\
DA59CBE8571796C\">3.1-3</a><br />\n<code class=\"func\">RatExpOnnLetters</code\
>  <a href=\"chap3_mj.html#X7EE5A70F7F237C41\">3.1-2</a><br />\n<code class=\"\
func\">RatExpToAut</code>  <a href=\"chap4_mj.html#X866BCCB2788E8561\">4.2-2</\
a><br />\n<code class=\"func\">RatExpToAutomaton</code>  <a href=\"chap4_mj.ht\
ml#X866BCCB2788E8561\">4.2-2</a><br />\n<code class=\"func\">RatExpToNDAut</co\
de>  <a href=\"chap4_mj.html#X840EEB7B7DD8B03D\">4.2-1</a><br />\nrational exp\
ressions  <a href=\"chap3_mj.html#X833D315483172905\">3.</a><br />\n<code clas\
s=\"func\">RationalExpression</code>  <a href=\"chap3_mj.html#X801EC6F38568426\
D\">3.1-1</a><br />\n<code class=\"func\">ReducedNFA</code>  <a href=\"chap5_m\
j.html#X83B0473278DC14F3\">5.1-4</a><br />\n<code class=\"func\">RemovedSinkSt\
ates</code>  <a href=\"chap2_mj.html#X8240136E7A26B1A6\">2.5-4</a><br />\n<cod\
e class=\"func\">ReversedAutomaton</code>  <a href=\"chap2_mj.html#X7C0526217B\
FE7A65\">2.5-5</a><br />\n<code class=\"func\">ReversedGraph</code>  <a href=\
\"chapA_mj.html#X7BA5F1DF7DA89DC5\">A.1-5</a><br />\n<code class=\"func\">SetF\
inalStatesOfAutomaton</code>  <a href=\"chap2_mj.html#X80689F1480F9D959\">2.2-\
7</a><br />\n<code class=\"func\">SetInitialStatesOfAutomaton</code>  <a href=\
\"chap2_mj.html#X8408FE8487028B7F\">2.2-5</a><br />\n<code class=\"func\">Size\
RatExp</code>  <a href=\"chap3_mj.html#X7E3AA84784019E6C\">3.1-4</a><br />\n<c\
ode class=\"func\">String</code>  <a href=\"chap2_mj.html#X81FB5BE27903EC32\">\
2.1-6</a><br />\n<code class=\"func\">SubgroupGenToInvAut</code>  <a href=\"ch\
apC_mj.html#X826D581D794F1BFB\">C.1-5</a><br />\n<code class=\"func\">Syntacti\
cSemigroupAut</code>  <a href=\"chap2_mj.html#X7E3F29DF86A26347\">2.6-2</a><br\
 />\n<code class=\"func\">SyntacticSemigroupLang</code>  <a href=\"chap2_mj.ht\
ml#X7D058F0D83D7B49B\">2.6-3</a><br />\n<code class=\"func\">TransitionMatrixO\
fAutomaton</code>  <a href=\"chap2_mj.html#X872BB42A81E4D0E7\">2.2-3</a><br />\
\n<code class=\"func\">TransitionSemigroup</code>  <a href=\"chap2_mj.html#X7B\
9994827CF94CC7\">2.6-1</a><br />\n<code class=\"func\">UnderlyingGraphOfAutoma\
ton</code>  <a href=\"chapA_mj.html#X78CF8E507E100C62\">A.1-9</a><br />\n<code\
 class=\"func\">UnderlyingMultiGraphOfAutomaton</code>  <a href=\"chapA_mj.htm\
l#X859B7C517AFBD198\">A.1-8</a><br />\n<code class=\"func\">UnionAutomata</cod\
e>  <a href=\"chap2_mj.html#X7A94A77A7C65BA90\">2.5-9</a><br />\n<code class=\
\"func\">UnionRatExp</code>  <a href=\"chap3_mj.html#X8206BD4E82A81D8F\">3.3-1\
</a><br />\n<code class=\"func\">UsefulAutomaton</code>  <a href=\"chap5_mj.ht\
ml#X7B5B5B10868FB525\">5.2-1</a><br />\n<code class=\"func\">VertexInDegree</c\
ode>  <a href=\"chapA_mj.html#X868EE741872B932D\">A.1-2</a><br />\n<code class\
=\"func\">VertexOutDegree</code>  <a href=\"chapA_mj.html#X84DF2E8E7A7B32C6\">\
A.1-3</a><br />\n", 
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M \"gapdoc.dtd\">\n\n  <?LaTeX ExtraPreamble=\"\\usepackage{graphicx}\"?>\n\n<\
Book Name=\"Automata\"> \n\n<TitlePage>\n  <Title>Automata</Title>\n  <Version\
>( Version \n1.13\n\n\n )\n  </Version>\n  <Author> Manuel Delgado \n    <Emai\
l>mdelgado@fc.up.pt</Email>\n    <Homepage>http://www.fc.up.pt/cmup/mdelgado</\
Homepage>\n  </Author>\n    <Author> Steve Linton\n    <Email>sal@cs.st-andrew\
s.ac.uk</Email>\n    <Homepage>http://www-circa.mcs.st-and.ac.uk/~sal/</Homepa\
ge>\n  </Author>\n  <Author> José Joäo Morais \n   <!-- <Email>josejoao@fc.u\
p.pt</Email>-->\n  </Author>\n  <Copyright> &copyright; 2004 by Manuel Delgado\
, Steve Linton and José Morais <P/>\n              We adopt the copyright reg\
ulations of &GAP; as detailed in the \n              copyright notice in the &\
GAP; manual. </Copyright>\n\n<Colophon>\n\nThis work started in 1998, when the\
 first author was in the\nLIAFA at the University of Paris 7, in a post-doc. \
\nEncouraged by J. E. Pin, he began the implementation in &GAP;3 of\nan algori\
thm obtained some time before to answer a question from the realm \nof Finite \
Semigroups proposed by J. Almeida. It is now part of a separate \npackage: <C>\
finsemi</C>. <P/>\n\nThe first version of this package on automata was prepare\
d by the first author \nwho gave it the form of a &GAP; share package.\nIn a s\
econd version, prepared by the first and third authors, \nmany functions have \
been added and the performance of many of the existing \nones has been improve\
d. Further important improvements, specially concerning performance,\nhave bee\
n achieved when the second author joined the group.\n<P/>\n\nSince Version 1.1\
2, the package is maintained by the first two authors.\n\nBug reports, suggest\
ions and comments are, of course, welcome. Please use our\nemail addresses to \
this effect.\n\n</Colophon>\n\n<Acknowledgements>\n\nThe first author wishes t\
o acknowledge Cyril Nicaud and Paulo Varandas for \ntheir help in programming \
some functions of the very first version of this \npackage. He wishes also to \
acknowledge useful discussions and comments by \nCyril Nicaud, Vítor H. Ferna\
ndes, Jean-Eric Pin and Jorge Almeida.\n<P/>\nThe first author also acknowledg\
es support of FCT through CMUP \nand the FCT and POCTI Project POCTI/32817/MAT\
/2000 which is funded in\ncooperation with the European Community Fund FEDER.\
\n<P/>\nThe third author acknowledges financial support of FCT and the POCTI p\
rogram \nthrough a scholarship given by Centro de Matemática da Universidade \
do Porto.\n<P/>\n\nThe authors would like to thank Mark Kambites for his contr\
ibution in finding bugs and making suggestions for the improvement of this pac\
kage.\n<P/>\n<P/>\n<P/>\nConcerning the mantainment:\n<P/>\n<P/>\nThe first au\
thor was/is (partially) supported by the FCT project PTDC/MAT/65481/2006 and a\
lso by the\n<E>Centro de Matemática da Universidade do\nPorto</E> (CMUP), fun\
ded by the European Regional Development Fund through the program COMPETE and \
by the Portuguese Government through the FCT - Fundaèäo para a Ciência e a \
Tecnologia under the project PEst-C/MAT/UI0144/2011.\n</Acknowledgements>\n\n<\
/TitlePage>\n\n<TableOfContents/>\n\n<Body>\n\n<?xml version=\"1.0\" encoding=\
\"UTF-8\"?>\n  <!-- $Id: introduction.xml,v 1.13  Exp $ -->\n  <Chapter>\n    \
<Heading>\n      Introduction\n    </Heading>\n    In many situations an autom\
aton is conveniently described through a diagram like the following\n    <P />\
\n    <Alt Only=\"LaTeX\">\n      \\begin{figure}[htbp] \\begin{center} \\leav\
evmode \\includegraphics[bb=0 0 132 279]{aut1} \\end{center} \\label{fig:aut1}\
 \\end{figure}\n    </Alt>\n    <Alt Only=\"HTML\">\n      &#60;br&#62;&#60;ce\
nter&#62;&#60;img src=&#34;aut1.gif&#34;&#62;&#60;/center&#62;&#60;br&#62;\n  \
  </Alt>\n    <P />\n    This diagram describes a (deterministic) automaton wi\
th\n    <M>\n      3\n    </M>\n    states (the elements of the set\n    <M>\n\
      \\{1,2,3\\}).\n    </M>\n    The arrow pointing to the state\n    <M>\n \
     1\n    </M>\n    indicates that\n    <M>\n      1\n    </M>\n    is the i\
nitial state and the two circles around state\n    <M>\n      3\n    </M>\n   \
 indicate that\n    <M>\n      3\n    </M>\n    is a final or accepting state.\
 The set\n    <M>\n      \\{a,b\\}\n    </M>\n    is the <E>alphabet</E> of th\
e automaton; its elements are called <E>letters</E> and are the labels of the \
edges of the diagram. The words\n    <M>\n      a\n    </M>\n    ,\n    <M>\n \
     ab^2\n    </M>\n    ,\n    <M>\n      b^5a^3b\n    </M>\n    are examples\
 of words recognized by the automaton since they are labels of paths from the \
initial to the final state.\n    <P />\n    The set of words recognized by an \
automaton is called the <E>language</E> of the automaton. It is a rational lan\
guage and may be represented through a rational expression. For instance, <Log\
>(aUb)(a(aUb)Ub(aUb))*</Log> is a rational expression representing the languag\
e of the above automaton. \n    <P />\nKleene's Theorem states that a language\
 is rational if and only if it is the language of a finite automaton.\nBoth di\
rections of Kleene's Theorem can be proved constructively, and these algorithm\
s, to go from an automaton to a rational expression and <E>vice-versa</E>, are\
 implemented in this package.\n    <P />\nOf course, one has to pay attention \
to the size of the output produced. When producing a deterministic automaton e\
quivalent to a given rational expression one can obtain an optimal solution (t\
he minimal automaton) using standard algorithms <Cite Key=\"AHU:74\"/>.\n    <\
P />\nWhen producing a rational expression for the language of an automaton, a\
nd taking into account some reasonable measure for the size of a rational expr\
ession, to determine a minimal one is apparently computationally difficult. We\
 use here some heuristic methods (to be published elsewhere) which in practice\
 lead to very reasonable results.\n    <P />\nThe development of this work has\
 benefited from the existence of AMoRE <Cite Key=\"AMORE:95\" />, a package wr\
itten in <C>C</C> to handle Automata, Monoids and Regular Expressions. In fact\
, its manual has been very useful and some of the algorithms implemented here \
are those implemented in AMoRE. In this package, unlike what happened with AMo\
RE, we do not have to worry about the monoid part in order to make it useful t\
o semigroup theorists, since monoids are already implemented in &GAP; and we m\
ay take advantage of this fact. We just need a function to compute the transit\
ion semigroup of an automaton.\n\n     <P />\n     <P />\nThe parts of this pa\
ckage that have not so directly to do with automata or rational expressions ar\
e put into appendices in this manual. Some words about these appendices follow\
.\n     <P />\nUsing the external program Graphviz <Cite Key=\"KoutsofiosNorth\
:2002\" /> to graph visualization, one can visualize automata. This very conve\
nient tool presently works easily under LINUX.\n     <P />\nGiven a finitely g\
enerated subgroup of the free group it is possible to compute a flower automat\
on and perform Stallings foldings over it in order to obtain an inverse automa\
ton corresponding to the given subgroup.\n     <P />\n  </Chapter>\n\n<?xml ve\
rsion=\"1.0\" encoding=\"UTF-8\"?>\n<!-- $Id: automata.xml,v 1.13  Exp $ -->\n\
\n<Chapter><Heading>Finite Automata</Heading>\n\nThis chapter describes the re\
presentations used in this package for\nfinite automata and some functions to \
determine information about them.\n<P/>\n We have to remark that the states of\
 an automaton are always named\n<M>1,2,3,\\ldots;</M> the alphabet may be give\
n by the user. By default \nit is <M>\\{a,b,c,\\ldots\\}</M> (or <M>\\{a_1,a_2\
,a_3,\\ldots\\}</M> in the \ncase of alphabets with more than <M>26</M> letter\
s). \n<P/>\nThe transition function of an automaton with <M>q</M> states over \
an alphabet with  <M> n</M> \nletters is represented by a (not necessarily den\
se) <M>n\\times q</M> \n matrix. Each row of the matrix describes the action o\
f the corresponding\nletter on the states.\nIn the case of a <Emph>determinist\
ic automaton</Emph> (DFA) the entries of the\n matrix are non-negative integer\
s. \nWhen all entries of the transition table \nare positive integers, the aut\
omaton is said to be \n<Emph>dense</Emph> or <Emph>complete</Emph>.\n<!--<Inde\
x>automaton!complete</Index><Index>automaton!dense</Index>-->\n\nIn the case o\
f a <Emph>non deterministic automaton</Emph> (NFA) the entries of the\n matrix\
 may be lists of non-negative integers. \n\n<Emph>Automata with <M>\\epsilon</\
M>-transitions</Emph> are also allowed: the \nlast letter of the alphabet is a\
ssumed to be  <M>\\epsilon</M> and is represented by @.\n\n<Section><Heading>A\
utomata generation</Heading>  \n<!-- In the case of <Emph>non\n deterministic \
automata</Emph> the entries of the matrix are lists of \nnon-negative integers\
. -->\n\nThe way to create an automaton in &GAP; is the following \n <ManSecti\
on>\n<Func Name=\"Automaton\" Arg=\"Type, Size, Alphabet,TransitionTable, \nIn\
itial, Accepting\"/>\n<Description>\n<!-- The names chosen for the arguments d\
escribe their meaning.-->\n<C>Type</C> may be \n<C>\"det\"</C>, <C>\"nondet\"<\
/C> or <C>\"epsilon\"</C> according to whether \nthe automaton is deterministi\
c, non deterministic or an automaton with \n<M>\\epsilon</M>-transitions. \n<C\
>Size</C> is a positive integer representing the\nnumber of states of the auto\
maton. <C>Alphabet</C> is the number of\nletters of the alphabet or a list wit\
h the letters of the ordered alphabet. \n<C>TransitionTable</C> is the transit\
ion matrix. The\nentries are non-negative integers not greater than the size o\
f the automaton.\nIn the case of non deterministic automata, lists of non-nega\
tive integers not \ngreater than the size of the automaton are also allowed. <\
C>Initial</C>\nand <C>Accepting</C> are, respectively, the lists of initial an\
d accepting\nstates.  \n<Example>\n<![CDATA[\ngap> aut:=Automaton(\"det\",4,2,\
[[3,,3,4],[3,4,0,4]],[1],[4]);\n< deterministic automaton on 2 letters with 4 \
states >\ngap> Display(aut);\n   |  1  2  3  4\n-----------------\n a |  3    \
 3  4\n b |  3  4     4\nInitial state:   [ 1 ]\nAccepting state: [ 4 ]\n]]>\n\
</Example>\nThe alphabet of the automaton may be specified:\n<Example><![CDATA\
[\ngap> aut:=Automaton(\"det\",4,\"01\",[[3,,3,4],[3,4,0,4]],[1],[4]);\n< dete\
rministic automaton on 2 letters with 4 states >\ngap> Display(aut);\n   |  1 \
 2  3  4\n-----------------\n 0 |  3     3  4\n 1 |  3  4     4\nInitial state\
:   [ 1 ]\nAccepting state: [ 4 ]\n]]></Example>\nInstead of leaving a hole in\
 the transition matrix, we may write a <C>0</C>\n to mean that no transition i\
s present. \nNon deterministic automata may be given the same way.\n<Example><\
![CDATA[\ngap> ndaut:=Automaton(\"nondet\",4,2,[[3,[1,2],3,0],[3,4,0,[2,3]]],[\
1],[4]);\n< non deterministic automaton on 2 letters with 4 states >\ngap> Dis\
play(ndaut);\n   |  1       2          3       4\n----------------------------\
-------------\n a | [ 3 ]   [ 1, 2 ]   [ 3 ]\n b | [ 3 ]   [ 4 ]              \
[ 2, 3 ]\nInitial state:   [ 1 ]\nAccepting state: [ 4 ]\n]]></Example>\nAlso \
in the same way can be given <M>\\epsilon</M>-automata. The letter <M>\\epsilo\
n</M> is written <C>@</C> instead.\n<Example><![CDATA[\ngap> x:=Automaton(\"ep\
silon\",3,\"01@\",[[,[2],[3]],[[1,3],,[1]],[[1],[2],\n> [2]]],[2],[2,3]);\n< e\
psilon automaton on 3 letters with 3 states >\ngap> Display(x);\n   |  1      \
    2       3\n------------------------------\n 0 |            [ 2 ]   [ 3 ]\n\
 1 | [ 1, 3 ]           [ 1 ]\n @ | [ 1 ]      [ 2 ]   [ 2 ]\nInitial state:  \
  [ 2 ]\nAccepting states: [ 2, 3 ]\n]]></Example>\nBigger automata are displa\
yed in another form:\n<Example><![CDATA[\ngap> aut:=Automaton(\"det\",16,2,[[4\
,0,0,6,3,1,4,8,7,4,3,0,6,1,6,0],\n> [3,4,0,0,6,1,0,6,1,6,1,6,6,4,8,7,4,5]],[1]\
,[4]);\n< deterministic automaton on 2 letters with 16 states >\ngap> Display(\
aut);\n1    a   4\n1    b   3\n2    b   4\n    ... some more lines\n15   a   6\
\n15   b   8\n16   b   7\nInitial state:   [ 1 ]\nAccepting state: [ 4 ]\n]]><\
/Example>\n</Description> </ManSection>\n\n<ManSection>\n<Func Name=\"IsAutoma\
ton\" Arg=\"O\"/>\n<Description>\nIn the presence of an object <A>O</A>, one m\
ay want to test whether \n<C>O</C> is an automaton. This may be done using the\
 function <C>IsAutomaton</C>.\n<Example><![CDATA[\ngap> x:=Automaton(\"det\",3\
,2,[ [ 0, 2, 0 ], [ 0, 1, 0 ] ],[ 3 ],[ 2 ]);;\ngap> IsAutomaton(x);\ntrue\n]]\
></Example>\n</Description> </ManSection>\n\n<ManSection>\n<Func Name=\"IsDete\
rministicAutomaton\" Arg=\"aut\"/>\n<Description>\nReturns <K>true</K> when <C\
>aut</C> is a deterministic automaton and <K>false</K> otherwise. \n<Example><\
![CDATA[\ngap> x:=Automaton(\"det\",3,2,[ [ 0, 2, 0 ], [ 0, 1, 0 ] ],[ 3 ],[ 2\
 ]);;\ngap> IsDeterministicAutomaton(x);\ntrue\n]]></Example>\n</Description> \
</ManSection>\n<!-- silentius -->\n<ManSection>\n<Func Name=\"IsNonDeterminist\
icAutomaton\" Arg=\"aut\"/>\n<Description>\nReturns <K>true</K> when <C>aut</C\
> is a non deterministic automaton and <K>false</K> otherwise. \n<Example><![C\
DATA[\ngap> y:=Automaton(\"nondet\",3,2,[[,[1,3],],[,[2,3],[1,3]]],[1,2],[1,3]\
);;\ngap> IsNonDeterministicAutomaton(y);\ntrue\n]]></Example>\n</Description>\
 </ManSection>\n\n<ManSection>\n<Func Name=\"IsEpsilonAutomaton\" Arg=\"aut\"/\
>\n<Description>\nReturns <K>true</K> when <C>aut</C> is an <M>\\epsilon</M>-a\
utomaton and <K>false</K> otherwise. \n<Example><![CDATA[\ngap> z:=Automaton(\
\"epsilon\",2,2,[[[1,2],],[[2],[1]]],[1,2],[1,2]);;\ngap> IsEpsilonAutomaton(z\
);\ntrue\n]]></Example>\n</Description> </ManSection>\n<ManSection>\n<Func Nam\
e=\"String\" Arg=\"aut\"/>\n<Description>\n\nThe way  &GAP; displays an automa\
ton is quite natural, but when one wants to \ndo small changes, for example us\
ing <E>copy/paste</E>, the use of the function \n<C>String</C> (possibly follo\
wed by <C>Print</C>) may be usefull.\n<Example><![CDATA[\ngap> x:=Automaton(\"\
det\",3,2,[ [ 0, 2, 0 ], [ 0, 1, 0 ] ],[ 3 ],[ 2 ]);;\ngap> String(x);\n\"Auto\
maton(\\\"det\\\",3,\\\"ab\\\",[ [ 0, 2, 0 ], [ 0, 1, 0 ] ],[ 3 ],[ 2 ]);;\"\n\
gap> Print(String(x));\nAutomaton(\"det\",3,\"ab\",[ [ 0, 2, 0 ], [ 0, 1, 0 ] \
],[ 3 ],[ 2 ]);;\n]]></Example>\n<Example><![CDATA[\ngap> z:=Automaton(\"epsil\
on\",2,2,[[[1,2],],[[2],[1]]],[1,2],[1,2]);;\ngap> Print(String(z));\nAutomato\
n(\"epsilon\",2,\"a@\",[ [ [ 1, 2 ], [ ] ], [ [ 2 ], [ 1 ] ] ],[ 1, 2 ],[ \\\n\
1, 2 ]);;\n]]></Example>\n</Description> </ManSection>\n\n<ManSection>\n<Func \
Name=\"RandomAutomaton\" Arg=\"Type, Size, Alphabet\"/>\n<Description>\nGiven \
the <A>Type</A>, the <A>Size</A> (i.e. the number of states) and the <A>Alphab\
et</A> (a positive integer\nor a list), returns a pseudo random automaton with\
 \nthese parameters.\n<Example><![CDATA[\ngap> RandomAutomaton(\"det\",5,\"ac\
\");\n< deterministic automaton on 2 letters with 5 states >\ngap> Display(las\
t);\n   |  1  2  3  4  5\n--------------------\n a |     2  3\n c |  2  3\nIni\
tial state:    [ 4 ]\nAccepting states: [ 3, 4 ]\n\ngap> RandomAutomaton(\"non\
det\",3,[\"a\",\"b\",\"c\"]);\n< non deterministic automaton on 3 letters with\
 3 states >\n\ngap> RandomAutomaton(\"epsilon\",2,\"abc\");\n< epsilon automat\
on on 4 letters with 2 states >\n\ngap> RandomAutomaton(\"epsilon\",2,2);\n< e\
psilon automaton on 3 letters with 2 states >\ngap> Display(last);\n   |  1   \
       2\n----------------------\n a | [ 1, 2 ]\n b | [ 2 ]      [ 1 ]\n @ | [\
 1, 2 ]\nInitial state:    [ 2 ]\nAccepting states: [ 1, 2 ]\n\ngap> a:=Random\
Transformation(3);;\ngap> b:=RandomTransformation(3);;\ngap> aut:=RandomAutoma\
ton(\"det\",4,[a,b]);\n< deterministic automaton on 2 letters with 4 states >\
\n]]></Example>\n</Description> </ManSection>\n\n</Section>\n\n\n<Section><Hea\
ding>Automata internals</Heading>\nIn this section we describe the functions u\
sed to access the internals of an automaton.\n\n<ManSection> \n<Func Name=\"Al\
phabetOfAutomaton\" Arg=\"aut\"/>\n<Description>\n\nReturns the number of symb\
ols in the alphabet of automaton <C>aut</C>.\n<Example><![CDATA[\ngap> aut:=Au\
tomaton(\"det\",4,2,[[3,,3,4],[3,4,0,]],[1],[4]);;\ngap> AlphabetOfAutomaton(a\
ut);\n2\n]]></Example>\n</Description> </ManSection>\n\n\n<ManSection> \n<Func\
 Name=\"AlphabetOfAutomatonAsList\" Arg=\"aut\"/>\n<Description>\n\nReturns th\
e alphabet of automaton <C>aut</C> always\nas a list.\n\n Note that when the a\
lphabet of the automaton is given as an integer \n(meaning the number of symbo\
ls) \nnot greater than 26 it returns the list <C>\"abcd....\"</C>.\nIf the alp\
habet is given by means of an integer greater than 26, the \nfunction returns \
<C>[ \"a1\", \"a2\", \"a3\", \"a4\", ... ]</C>.\n<Example><![CDATA[\ngap> a:=R\
andomAutomaton(\"det\",5,\"cat\");\n< deterministic automaton on 3 letters wit\
h 5 states >\ngap> AlphabetOfAutomaton(a);\n3\ngap> AlphabetOfAutomatonAsList(\
a);\n\"cat\"\ngap> a:=RandomAutomaton(\"det\",5,20);\n< deterministic automato\
n on 20 letters with 5 states >\ngap> AlphabetOfAutomaton(a);\n20\ngap> Alphab\
etOfAutomatonAsList(a);\n\"abcdefghijklmnopqrst\"\ngap> a:=RandomAutomaton(\"d\
et\",5,30);\n< deterministic automaton on 30 letters with 5 states >\ngap> Alp\
habetOfAutomaton(a);\n30\ngap> AlphabetOfAutomatonAsList(a);\n[ \"a1\", \"a2\"\
, \"a3\", \"a4\", \"a5\", \"a6\", \"a7\", \"a8\", \"a9\", \"a10\", \"a11\", \n\
  \"a12\", \"a13\", \"a14\", \"a15\", \"a16\", \"a17\", \"a18\", \"a19\", \"a2\
0\", \"a21\",\n  \"a22\", \"a23\", \"a24\", \"a25\", \"a26\", \"a27\", \"a28\"\
, \"a29\", \"a30\" ]\n]]></Example>\n</Description> </ManSection>\n\n\n\n<ManS\
ection> \n<Func Name=\"TransitionMatrixOfAutomaton\" Arg=\"aut\"/>\n<Descripti\
on>\n\nReturns the transition matrix of automaton <C>aut</C>.\n<Example><![CDA\
TA[\ngap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[3,4,0,]],[1],[4]);;\ngap> Tran\
sitionMatrixOfAutomaton(aut);\n[ [ 3, 0, 3, 4 ], [ 3, 4, 0, 0 ] ]\n]]></Exampl\
e>\n</Description> </ManSection>\n\n\n<ManSection> \n<Func Name=\"InitialState\
sOfAutomaton\" Arg=\"aut\"/>\n<Description>\n\nReturns the initial states of a\
utomaton <C>aut</C>.\n<Example><![CDATA[\ngap> aut:=Automaton(\"det\",4,2,[[3,\
,3,4],[3,4,0,]],[1],[4]);;\ngap> InitialStatesOfAutomaton(aut);\n[ 1 ]\n]]></E\
xample>\n</Description> </ManSection>\n\n\n<ManSection> \n<Func Name=\"SetInit\
ialStatesOfAutomaton\" Arg=\"aut, I\"/>\n<Description>\n\nSets the initial sta\
tes of automaton <C>aut</C>.\n<C>I</C> may be a positive integer or a list of \
positive integers.\n<Example><![CDATA[\ngap> aut:=Automaton(\"det\",4,2,[[3,,3\
,4],[3,4,0,]],[1],[4]);;\ngap> SetInitialStatesOfAutomaton(aut,4);\ngap> Initi\
alStatesOfAutomaton(aut);\n[ 4 ]\ngap> SetInitialStatesOfAutomaton(aut,[2,3]);\
\ngap> InitialStatesOfAutomaton(aut);\n[ 2, 3 ]\n]]></Example>\n</Description>\
 </ManSection>\n\n\n<ManSection> \n<Func Name=\"FinalStatesOfAutomaton\" Arg=\
\"aut\"/>\n<Description>\n\nReturns the final states of automaton <C>aut</C>.\
\n<Example><![CDATA[\ngap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[3,4,0,]],[1],\
[4]);;\ngap> FinalStatesOfAutomaton(aut);\n[ 4 ]\n]]></Example>\n</Description\
> </ManSection>\n\n\n<ManSection> \n<Func Name=\"SetFinalStatesOfAutomaton\" A\
rg=\"aut, F\"/>\n<Description>\n\nSets the final states of automaton <C>aut</C\
>.\n<C>F</C> may be a positive integer or a list of positive integers.\n<Examp\
le><![CDATA[\ngap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[3,4,0,]],[1],[4]);;\n\
gap> FinalStatesOfAutomaton(aut);\n[ 4 ]\ngap> SetFinalStatesOfAutomaton(aut,2\
);\ngap> FinalStatesOfAutomaton(aut);\n[ 2 ]\n]]></Example>\n</Description> </\
ManSection>\n\n\n<ManSection> \n<Func Name=\"NumberStatesOfAutomaton\" Arg=\"a\
ut\"/>\n<Description>\n\nReturns the number of states of automaton <C>aut</C>.\
\n<Example><![CDATA[\ngap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[3,4,0,]],[1],\
[4]);;\ngap> NumberStatesOfAutomaton(aut);\n4\n]]></Example>\n</Description> <\
/ManSection>\n\n</Section>\n\n\n\n<Section><Heading>Comparison of automata</He\
ading>\nAlthough there is no standard way to compare automata it is usefull to\
 be able to do some kind of comparison. Doing so, one can consider sets of aut\
omata.\n We just compare the strings of the automata.\n<Log>\ngap> x:=Automato\
n(\"det\",3,2,[ [ 0, 2, 0 ], [ 0, 1, 0 ] ],[ 3 ],[ 2 ]);;\ngap> y:=Automaton(\
\"det\",3,2,[ [ 2, 0, 0 ], [ 1, 3, 0 ] ],[ 3 ],[ 2, 3 ]);;\ngap> x=y;\nfalse\n\
gap> Size(Set([y,x,x]));\n2\n</Log>\n</Section>\n<Section><Heading>Tests invol\
ving automata</Heading>\n\nThis section describes some useful tests involving \
automata.\n\n<ManSection> \n<Func Name=\"IsDenseAutomaton\" Arg=\"aut\"/>\n<De\
scription>\n\nTests whether a deterministic automaton <C>aut</C> is complete. \
\n(See also <Ref Func=\"NullCompletionAutomaton\"/>.)  \n<Example><![CDATA[\ng\
ap> aut:=Automaton(\"det\",4,2,[[3,,3,4],[3,4,0,]],[1],[4]);;\ngap> IsDenseAut\
omaton(aut);                                 \nfalse\n]]></Example>\n</Descrip\
tion> </ManSection>\n\n<ManSection> \n<Func Name=\"IsRecognizedByAutomaton\" A\
rg=\"A,w\"/>\n<Description>\nThe arguments are: an automaton <A>A</A> and a st\
ring (i.e. a word) <A>w</A> in the alphabet of the automaton. \nReturns <C>tru\
e</C> if the word is recognized by the automaton \n and <C>false</C> otherwise\
. \n\n<Example><![CDATA[\ngap> aut:=Automaton(\"det\",3,2,[[1,2,1],[2,1,3]],[1\
],[2]);;\ngap> IsRecognizedByAutomaton(aut,\"bbb\");\ntrue\n\ngap> aut:=Automa\
ton(\"det\",3,\"01\",[[1,2,1],[2,1,3]],[1],[2]);;\ngap> IsRecognizedByAutomato\
n(aut,\"111\");\ntrue\n]]></Example>\n</Description> </ManSection>\n\n\n<ManSe\
ction>\n<Func Name=\"IsPermutationAutomaton\" Arg=\"aut\"/>\n<Description>\nTh\
e argument is a deterministic automaton. Returns <K>true</K> when each letter \
of the alphabet induces a permutation on the vertices and <K>false</K> otherwi\
se. <Example><![CDATA[\ngap> x:=Automaton(\"det\",3,2,[ [ 1, 2, 3 ], [ 1, 2, 3\
 ] ],[ 1 ],[ 2, 3 ]);;\ngap> IsPermutationAutomaton(x);\ntrue\n]]></Example>\n\
</Description> </ManSection>\n\n<ManSection>\n<Func Name=\"IsInverseAutomaton\
\" Arg=\"aut\"/>\n<Description>\nThe argument is a deterministic automaton. Re\
turns <K>true</K> when each letter of the alphabet induces an injective partia\
l function on the vertices and <K>false</K> otherwise. <Example><![CDATA[\ngap\
> x:=Automaton(\"det\",3,2,[ [ 0, 1, 3 ], [ 0, 1, 2 ] ],[ 2 ],[ 1 ]);;\ngap> I\
sInverseAutomaton(x);\ntrue\n]]></Example>\n\nFrequently an inverse automaton \
is thought as if the inverse edges (labeled by formal inverses of the letters \
of the alphabet) were present, although they are usually not explicited. They \
can be made explicit using the function <C>AddInverseEdgesToInverseAutomaton</\
C>\n</Description> </ManSection>\n\n<ManSection>\n<Func Name=\"AddInverseEdges\
ToInverseAutomaton\" Arg=\"aut\"/>\n<Description>\nThe argument is an inverse \
automaton over the alphabet <M>\\{a,b,c,\\ldots\\}</M>. Returns an automaton w\
ith the inverse edges added. (The formal inverse of a letter is represented by\
 the corresponding capital letter.)\n <Example><![CDATA[\ngap> x:=Automaton(\"\
det\",3,2,[[ 0, 1, 3 ],[ 0, 1, 2 ]],[ 2 ],[ 1 ]);;Display(x);\n   |  1  2  3\n\
--------------\n a |     1  3\n b |     1  2\nInitial state:   [ 2 ]\nAcceptin\
g state: [ 1 ]\ngap> AddInverseEdgesToInverseAutomaton(x);Display(x);\n   |  1\
  2  3\n--------------\n a |     1  3\n b |     1  2\n A |  2     3\n B |  2  \
3\nInitial state:   [ 2 ]\nAccepting state: [ 1 ]\n]]></Example>\n</Descriptio\
n> </ManSection>\n\n<ManSection>\n<Func Name=\"IsReversibleAutomaton\" Arg=\"a\
ut\"/>\n<Description>\nThe argument is a deterministic automaton. \nReturns <K\
>true</K> when <A>aut</A> is a reversible automaton, i.e. the automaton obtain\
ed by reversing all edges and switching the initial and final states \n(see al\
so <Ref Func=\"ReversedAutomaton\"/>) is deterministic. Returns <K>false</K> o\
therwise.\n<Example><![CDATA[\ngap> x:=Automaton(\"det\",3,2,[ [ 0, 1, 2 ], [ \
0, 1, 3 ] ],[ 2 ],[ 2 ]);;\ngap> IsReversibleAutomaton(x);\ntrue\n]]></Example\
>\n</Description> </ManSection>\n\n</Section>\n\n<Section><Heading>Basic opera\
tions</Heading>\n\n\n<ManSection>\n<Func Name=\"CopyAutomaton\" Arg=\"aut\"/>\
\n<Description>\nReturns a new automaton, which is a copy of automaton <A>aut<\
/A>.\n </Description> </ManSection>  \n\n\n <ManSection> \n<Func Name=\"NullCo\
mpletionAutomaton\" Arg=\"aut\"/>\n<Description>\n\n<C>aut</C> is a determinis\
tic automaton. If it is complete returns <A>aut</A>,\notherwise returns the co\
mpletion (with a null state) of <A>aut</A>. Notice that the words recognized b\
y  <A>aut</A> and its completion are the same.\n<Example><![CDATA[\ngap> aut:=\
Automaton(\"det\",4,2,[[3,,3,4],[2,4,4,]],[1],[4]);;\ngap> IsDenseAutomaton(au\
t);\nfalse\ngap> y:=NullCompletionAutomaton(aut);;Display(y);\n   |  1  2  3  \
4  5\n--------------------\n a |  3  5  3  4  5\n b |  2  4  4  5  5\nInitial \
state:   [ 1 ]\nAccepting state: [ 4 ]\n]]></Example>\n\nThe state added is a \
<Emph>sink state</Emph> i.e. it is a state <M>q</M> which is not initial nor a\
ccepting and for all letter <M>a</M> in the alphabet of the automaton, <M>q</M\
> is the result of the action of <M>a</M>  in <M>q</M>. (Notice that reading \
\na word, one does not go out of a sink state.) \n </Description> </ManSection\
>  \n\n<ManSection>\n<Func Name=\"ListSinkStatesAut\" Arg=\"aut\"/>\n<Descript\
ion>\nComputes the list of all sink states of the automaton <A>aut</A>.\n<Exam\
ple><![CDATA[\ngap> x:=Automaton(\"det\",3,2,[ [ 2, 3, 3 ], [ 1, 2, 3 ] ],[ 1 \
],[ 2, 3 ]);;\ngap> ListSinkStatesAut(x);\n[  ]\ngap> y:=Automaton(\"det\",3,2\
,[ [ 2, 3, 3 ], [ 1, 2, 3 ] ],[ 1 ],[ 2 ]);;\ngap> ListSinkStatesAut(y);\n[ 3 \
]\n]]></Example>\n </Description> </ManSection>  \n\n<ManSection>\n<Func Name=\
\"RemovedSinkStates\" Arg=\"aut\"/>\n<Description>\nRemoves all sink states of\
 the automaton <A>aut</A>.\n<Example><![CDATA[\ngap> y:=Automaton(\"det\",3,2,\
[[ 2, 3, 3 ],[ 1, 2, 3 ]],[ 1 ],[ 2 ]);;Display(y);\n   |  1  2  3\n----------\
----\n a |  2  3  3\n b |  1  2  3\nInitial state:   [ 1 ]\nAccepting state: [\
 2 ]\ngap> x := RemovedSinkStates(y);Display(x);\n< deterministic automaton on\
 2 letters with 2 states >\n   |  1  2\n-----------\n a |  2\n b |  1  2\nInit\
ial state:   [ 1 ]\nAccepting state: [ 2 ]\n]]></Example>\n </Description> </M\
anSection>  \n\n<ManSection>\n<Func Name=\"ReversedAutomaton\" Arg=\"aut\"/>\n\
<Description>\nInverts the arrows of the automaton <A>aut</A>.\n<Example><![CD\
ATA[\ngap> y:=Automaton(\"det\",3,2,[ [ 2, 3, 3 ], [ 1, 2, 3 ] ],[ 1 ],[ 2 ]);\
;\ngap> z:=ReversedAutomaton(y);;Display(z);\n   |  1       2       3\n-------\
-----------------------\n a |         [ 1 ]   [ 2, 3 ]\n b | [ 1 ]   [ 2 ]   [\
 3 ]\nInitial state:   [ 2 ]\nAccepting state: [ 1 ]\n]]></Example>\n </Descri\
ption> </ManSection>  \n\n\n<ManSection>\n<Func Name=\"PermutedAutomaton\" Arg\
=\"aut, p\"/>\n<Description>\nGiven an automaton <A>aut</A> and a list <A>p</A\
> representing a permutation of the states,\noutputs the equivalent permuted a\
utomaton.\n<Example><![CDATA[\ngap> y:=Automaton(\"det\",4,2,[[2,3,4,2],[0,0,0\
,1]],[1],[3]);;Display(y);\n   |  1  2  3  4\n-----------------\n a |  2  3  4\
  2\n b |           1\nInitial state:   [ 1 ]\nAccepting state: [ 3 ]\ngap> Di\
splay(PermutedAutomaton(y, [3,2,4,1]));\n   |  1  2  3  4\n-----------------\n\
 a |  2  4  2  1\n b |  3\nInitial state:   [ 3 ]\nAccepting state: [ 4 ]\n]]>\
</Example>\n </Description> </ManSection>  \n\n\n\n<ManSection>\n<Func Name=\"\
ListPermutedAutomata\" Arg=\"aut\"/>\n<Description>\nGiven an automaton <A>aut\
</A>, returns a list of automata with permuted states\n<Example><![CDATA[\ngap\
> x:=Automaton(\"det\",3,2,[ [ 0, 2, 3 ], [ 1, 2, 3 ] ],[ 1 ],[ 2, 3 ]);;\ngap\
> ListPermutedAutomata(x);\n[ < deterministic automaton on 2 letters with 3 st\
ates >, \n  < deterministic automaton on 2 letters with 3 states >, \n  < dete\
rministic automaton on 2 letters with 3 states >, \n  < deterministic automato\
n on 2 letters with 3 states >, \n  < deterministic automaton on 2 letters wit\
h 3 states >, \n  < deterministic automaton on 2 letters with 3 states > ]\n]]\
></Example>\n </Description> </ManSection> \n \n\n<ManSection>\n<Func Name=\"N\
ormalizedAutomaton\" Arg=\"A\"/>\n<Description>\nProduces an equivalent automa\
ton but in which the initial state is numbered 1 and the accepting states have\
 the greatest numbers.\n<Example><![CDATA[\ngap> x:=Automaton(\"det\",3,2,[[ 1\
, 2, 0 ],[ 0, 1, 2 ]],[2],[1, 2]);;Display(x);\n   |  1  2  3\n--------------\
\n a |  1  2\n b |     1  2\nInitial state:    [ 2 ]\nAccepting states: [ 1, 2\
 ]\ngap> Display(NormalizedAutomaton(x));\n   |  1  2  3\n--------------\n a |\
  1     3\n b |  3  1\nInitial state:    [ 1 ]\nAccepting states: [ 3, 1 ]\n]]\
></Example>\n </Description> </ManSection>  \n\n<ManSection>\n<Func Name=\"Uni\
onAutomata\" Arg=\"A,B\"/>\n<Description>\nProduces the disjoint union of the \
deterministic or non deterministic automata <C>A</C> and <C>B</C>. The output \
is a non-deterministic automaton.\n<Example><![CDATA[\ngap> x:=Automaton(\"det\
\",3,2,[ [ 1, 2, 0 ], [ 0, 1, 2 ] ],[ 2 ],[ 1, 2 ]);;\ngap> y:=Automaton(\"det\
\",3,2,[ [ 0, 1, 3 ], [ 0, 0, 0 ] ],[ 1 ],[ 1, 2, 3 ]);;\ngap> UnionAutomata(x\
,y);\n< non deterministic automaton on 2 letters with 6 states >\ngap> Display\
(last);\n   |  1       2       3       4    5       6\n-----------------------\
-------------------------\n a | [ 1 ]   [ 2 ]                [ 4 ]   [ 6 ]\n b\
 |         [ 1 ]   [ 2 ]\nInitial states:   [ 2, 4 ]\nAccepting states: [ 1, 2\
, 4, 5, 6 ]\n]]></Example>\n </Description> </ManSection>  \n\n<ManSection> \n\
<Func Name=\"ProductAutomaton\" Arg=\"A1,A2\"/>\n<Description>\nThe arguments \
must be deterministic automata. Returns the product of <A>A1</A> and <A>A2</A>\
. \n<P/>\n Note: <M>(p,q)->(p-1)m+q</M> is a bijection from <M>\\{1,\\ldots, n\
\\}\\times \\{1,\\ldots, m\\}</M> to <M>\\{1,\\ldots,mn\\}</M>.\n<Example><![C\
DATA[\ngap> x:=RandomAutomaton(\"det\",3,2);;Display(x);\n   |  1  2  3\n-----\
---------\n a |  2  3\n b |     1\nInitial state:    [ 3 ]\nAccepting states: \
[ 1, 2, 3 ]\ngap> y:=RandomAutomaton(\"det\",3,2);;Display(y);\n   |  1  2  3\
\n--------------\n a |     1\n b |  1  3\nInitial state:    [ 3 ]\nAccepting s\
tates: [ 1, 3 ]\ngap> z:=ProductAutomaton(x, y);;Display(z);\n   |  1  2  3  4\
  5  6  7  8  9\n--------------------------------\n a |     4        7\n b |  \
         1  3\nInitial state:    [ 9 ]\nAccepting states: [ 1, 3, 4, 6, 7, 9 ]\
\n]]></Example>\n</Description> \n</ManSection> \n\n\n<ManSection> \n<Func Nam\
e=\"ProductOfLanguages\" Arg=\"A1,A2\"/>\n<Description>\nGiven two regular lan\
guages (as automata or rational expressions),\nreturns an automaton that recog\
nizes the concatenation of the given \nlanguages, that is, the set of words <M\
>uv</M> such that\n<M>u</M> belongs to the first language and <M>v</M>\nbelong\
s to the second language.\n<Example><![CDATA[\ngap> a1:=ListOfWordsToAutomaton\
(\"ab\",[\"aa\",\"bb\"]);\n< deterministic automaton on 2 letters with 5 state\
s >\ngap> a2:=ListOfWordsToAutomaton(\"ab\",[\"a\",\"b\"]);\n< deterministic a\
utomaton on 2 letters with 3 states >\ngap> ProductOfLanguages(a1,a2);\n< dete\
rministic automaton on 2 letters with 5 states >\ngap> FAtoRatExp(last);\n(bbU\
aa)(aUb)\n]]></Example>\n</Description> \n</ManSection> \n\n\n</Section>\n<Sec\
tion><Heading>Links with Semigroups</Heading>\n\nEach letter of the alphabet o\
f an automaton induces a partial transformation in its set of \nstates. The se\
migroup generated by these transformations is\ncalled the <E>transition semigr\
oup</E> of the automaton.\n\n<ManSection> \n<Func Name=\"TransitionSemigroup\"\
 Arg=\"aut\"/>\n<Description>\n\nReturns the transition semigroup of the deter\
ministic automaton <A>aut</A>.\n<Example><![CDATA[\ngap> aut := Automaton(\"de\
t\",10,2,[[7,5,7,5,4,9,10,9,10,9],\n> [8,6,8,9,9,1,3,1,9,9]],[2],[6,7,8,9,10])\
;;\ngap> s := TransitionSemigroup(aut);;       \ngap> Size(s);                \
                                                  \n30\n]]></Example>\n\nThe t\
ransition semigroup of the minimal automaton recognizing a language is\nthe {\
\\it syntactic semigroup} of that language.\n\n </Description> </ManSection>  \
\n<ManSection> \n<Func Name=\"SyntacticSemigroupAut\" Arg=\"aut\"/>\n<Descript\
ion>\n\nReturns the syntactic semigroup of the  deterministic automaton <A>aut\
</A> (i.e. the transition semigroup of the equivalent minimal automaton)\nwhen\
 it is non empty and returns <K>fail</K> otherwise. \n<Example><![CDATA[\ngap>\
 x:=Automaton(\"det\",3,2,[ [ 1, 2, 0 ], [ 0, 1, 2 ] ],[ 2 ],[ 1, 2 ]);;\ngap>\
 S:=SyntacticSemigroupAut(x);;\ngap> Size(S);\n3\n]]></Example>\n</Description\
> </ManSection> \n<ManSection> \n<Func Name=\"SyntacticSemigroupLang\" Arg=\"r\
at\"/>\n<Description>\nReturns the syntactic semigroup of the language given b\
y the rational expression <A>rat</A>.\n<Example><![CDATA[\ngap> rat := Rationa\
lExpression(\"a*ba*ba*(@Ub)\");;\ngap> S:=SyntacticSemigroupLang(rat);;\ngap> \
Size(S);\n7\n]]></Example>\n</Description> </ManSection> \n</Section>\n  </Cha\
pter>\n\n\n\n<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<!-- $Id: rational.xm\
l,v 1.13  Exp $ -->\n\n<Chapter><Heading>Rational languages</Heading>\nRationa\
l languages are conveniently represented through rational expressions. These a\
re finite expressions involving letters of the alphabet; <C>concatenation</C>,\
 corresponding to the <E>product</E>; the symbol <C>U</C>, corresponding to th\
e <E>union</E>; and  the symbol <C>*</C>, corresponding to the Kleene's star.\
\n<Index>rational expressions</Index>\n\n<Section><Heading>Rational Expression\
s</Heading>\nThe expressions <C>@</C> and <C>\"empty\\_set\"</C> are used to r\
epresent the empty word and the empty set respectively.\n\n\n <ManSection> \n<\
Func Name=\"RationalExpression\" Arg=\" expr[, alph] \"/>\n<Description>\nA ra\
tional expression can be created using the function <C>RationalExpression</C>.\
 <A>expr</A> is a string representing the desired expression literally and <A>\
alph</A> (may or may not be present) is the alphabet of the expression. Of cou\
rse <A>alph</A> must not contain the symbols '@', '(', ')', '*' nor 'U'. When \
<A>alph</A> is not present, the alphabet of the rational expression is the set\
 of symbols (other than '\"', etc...) occurring in the expression. (The alphab\
et is then ordered with the alphabetical order.)\n<Example><![CDATA[\ngap> Rat\
ionalExpression(\"abUc\");\nabUc\ngap> RationalExpression(\"ab*Uc\");\nab*Uc\n\
gap> RationalExpression(\"001U1*\");\n001U1*\ngap> RationalExpression(\"001U1*\
\",\"012\");\n001U1*\n]]></Example>\n</Description>\n</ManSection>\n\n\n <ManS\
ection> \n<Func Name=\"RatExpOnnLetters\" Arg=\" n, operation, list \"/>\n<Des\
cription>\nThis is another way to construct a rational expression over an alph\
abet. The user may specify the alphabet or just give the number <M>n</M> of le\
tters (in this case the alphabet <M>\\{a,b,c,\\ldots\\}</M> is considered).  <\
A>operation</A> is the name of an operation, the possibilities\nbeing: <C>prod\
uct</C>, <C>union</C> or <C>star</C>. <A>list</A> is a list\n of rational expr\
essions, a rational expression in the case of\n``star'', or a \nlist consistin\
g of an integer when the rational expression is a single\nletter. The empty li\
st <C>[  ]</C> and <C>empty\\_set</C> are other possibilities for\n<C>list</C>\
. \n\nAn example follows\n<Example><![CDATA[\ngap> RatExpOnnLetters(2,\"star\"\
,RatExpOnnLetters(2,\"product\",\n> [RatExpOnnLetters(2,[],[1]),RatExpOnnLette\
rs(2,\"union\",\n> [RatExpOnnLetters(2,[],[1]),RatExpOnnLetters(2,[],[2])])]))\
;      \n(a(aUb))*\n]]></Example>\n \nThe empty word and the empty set are the\
 rational expressions:\n<Example><![CDATA[\ngap> RatExpOnnLetters(2,[],[]);   \
      \n@\ngap> RatExpOnnLetters(2,[],\"empty_set\");\nempty_set\n]]></Example\
>\n </Description></ManSection> \n\n<ManSection> \n<Func Name=\"RandomRatExp\"\
 Arg=\"arg\"/>\n<Description>\nGiven the number of symbols of the alphabet and\
 (possibly) a factor <M>m</M> which is intended to increase the randomality of\
 the expression,\nreturns a pseudo random rational expression over that alphab\
et.\n<Example><![CDATA[\ngap> RandomRatExp(2);\nb*(@Ua)\ngap> RandomRatExp(\"0\
1\");\nempty_set\ngap> RandomRatExp(\"01\");\n(0U1)*\ngap> RandomRatExp(\"01\"\
,7);\n0*1(@U0U1)\n]]></Example>\n</Description> \n</ManSection> \n\n<ManSectio\
n> \n<Func Name=\"SizeRatExp\" Arg=\"r\"/>\n<Description>\nReturns the size, i\
.e. the number of symbols of the alphabet, of the rational expression <A>r</A>\
.\n<Example><![CDATA[\ngap> a:=RationalExpression(\"0*1(@U0U1)\");\n0*1(@U0U1)\
\ngap> SizeRatExp(a);\n5\n]]></Example>\n</Description> \n</ManSection> \n\n<M\
anSection> \n<Func Name=\"IsRationalExpression\" Arg=\"r\"/>\n<Description>\nT\
ests whether an object is a rational expression.\n<Example><![CDATA[\ngap> r :\
= RandomRatExp(\"01\",7);\n1(0U1)U@\ngap> IsRatExpOnnLettersObj(r) and IsRatio\
nalExpressionRep(r);\ntrue\ngap> IsRationalExpression(RandomRatExp(\"01\"));\n\
true\n]]></Example>\n</Description> \n</ManSection> \n\n<ManSection> \n<Func N\
ame=\"AlphabetOfRatExp\" Arg=\"R\"/>\n<Description>\n\nReturns the number of s\
ymbols in the alphabet of the rational expression <C>R</C>.\n<Example><![CDATA\
[\ngap> r:=RandomRatExp(2);\na*(ba*U@)\ngap> AlphabetOfRatExp(r);\n2\ngap> r:=\
RandomRatExp(\"01\");\n1*(01*U@)\ngap> AlphabetOfRatExp(r);\n2\ngap> a:=Random\
Transformation(3);;\ngap> b:=RandomTransformation(3);;\ngap> r:=RandomRatExp([\
a,b]);\n(Transformation( [ 1, 1, 3 ] )UTransformation( [ 1, 1, 2 ] ))*\ngap> A\
lphabetOfRatExp(r);\n2\n]]></Example>\n</Description> </ManSection>\n\n\n<ManS\
ection> \n<Func Name=\"AlphabetOfRatExpAsList\" Arg=\"R\"/>\n<Description>\n\n\
Returns the alphabet of the rational expression <C>R</C> always\nas a list.\nI\
f the alphabet of the rational expression is given by means of an integer\nles\
s than 27 it returns the list <C>\"abcd....\"</C>,\notherwise returns <C>[ \"a\
1\", \"a2\", \"a3\", \"a4\", ... ]</C>.\n<Example><![CDATA[\ngap> r:=RandomRat\
Exp(2);\n(aUb)((aUb)(bU@)U@)U@\ngap> AlphabetOfRatExpAsList(r);\n\"ab\"\ngap> \
r:=RandomRatExp(\"01\");\n1*(0U@)\ngap> AlphabetOfRatExpAsList(r);\n\"01\"\nga\
p> r:=RandomRatExp(30);;\ngap> AlphabetOfRatExpAsList(r);\n[ \"a1\", \"a2\", \
\"a3\", \"a4\", \"a5\", \"a6\", \"a7\", \"a8\", \"a9\", \"a10\", \"a11\", \n\"\
a12\", \"a13\", \"a14\", \"a15\", \"a16\", \"a17\", \"a18\", \"a19\", \"a20\",\
 \"a21\", \n\"a22\", \"a23\", \"a24\", \"a25\", \"a26\", \"a27\", \"a28\", \"a\
29\", \"a30\" ]\n]]></Example>\n</Description> </ManSection>\n\n\n<ManSection>\
 \n<Func Name=\"CopyRatExp\" Arg=\"R\"/>\n<Description>\nReturns a new rationa\
l expression, which is a copy of <C>R</C>.\n<Example><![CDATA[\ngap> r:=Random\
RatExp(2);\na*(bU@)\ngap> CopyRatExp(r);\na*(bU@)\n]]></Example>\n</Descriptio\
n> </ManSection>\n\n    </Section>\n\n<Section><Heading>Comparison of rational\
 expressions</Heading>\nThe way two rational expressions <C>r1</C> and <C>r2</\
C> are compared through the\n<Alt Only=\"LaTeX\">\n$<![CDATA[<]]>$\n</Alt>\n<A\
lt Only=\"HTML\">\n&lt;\n</Alt> operator is the following:\nthe empty set is l\
esser than everything else;\nif r1 and r2 are letters, then the lesser is take\
n from the order in the alphabet;\nif r1 is a letter an r2 a product, union or\
 star, then r1 is lesser than r2;\na star expression is considered to be lesse\
r than a product or union expression\nand a product lesser than a union;\nto c\
ompare two star expressions we compare the expressions under the stars;\nto co\
mpare two product or union expressions we compare the subexpressions of\neach \
expression from left to right;\n</Section>\n\n\n<Section><Heading>Operations w\
ith rational languages</Heading>\n\nOnly operations with rational languages ov\
er the same alphabet are allowed.\n<P/>\nWe may compute expressions for the \n\
<C>product</C>, <C>union</C> and <C>star</C> (i.e.,\nsubmonoid generated by) o\
f rational sets. In some cases,\nsimpler expressions representing the same set\
 are returned.    \nNote that that two simplifications are always made, namely\
,\n<Alt Only=\"LaTeX\">\n$r\\cup\"empty_set\" = r$\n</Alt>\n<Alt Only=\"HTML\"\
>\nrU\"empty_set\" = r\n</Alt>\n and \n<Alt Only=\"LaTeX\">\n$r\\epsilon = r$\
\n</Alt>\n<Alt Only=\"HTML\">\nr@ = r\n</Alt>.\n\n\nOf course, these operation\
s may be used to construct more complex\nexpressions. \n\nFor rational express\
ions we have the functions <C>UnionRatExp</C>, <C>ProductRatExp</C>, <C>StarRa\
tExp</C>, that return respectively rational expressions for the <E>union</E> a\
nd <E>product</E> of \nthe languages given by the rational expressions <C>r</C\
> and <C>s</C> and the <C>star</C> of\nthe language given by the rational expr\
ession <C>r</C>.\n<ManSection> \n<Func Name=\"UnionRatExp\" Arg=\"r,s\"/>\n </\
ManSection> \n\n <ManSection> \n<Func Name=\"ProductRatExp\" Arg=\"r,s\"/>\n <\
/ManSection> \n\n <ManSection> \n<Func Name=\" StarRatExp\" Arg=\"r\"/>\n<Desc\
ription>\n\n\nThe expression <C>(a(aUb))*</C> may be produced in the following\
 way\n<Example><![CDATA[\ngap> r1 := RatExpOnnLetters(2,[],[1]); \na\ngap> r2 \
:= RatExpOnnLetters(2,[],[2]);\nb\ngap> r3 := UnionRatExp(r1,r2);\naUb\ngap> r\
4 := ProductRatExp(r1,r3);\na(aUb)\ngap> r5 := StarRatExp(r4);\n(a(aUb))*\n]]>\
</Example>\n</Description></ManSection> \n</Section>\n  </Chapter>\n\n\n<?xml \
version=\"1.0\" encoding=\"UTF-8\"?>\n<!-- $Id: aut-vs-rat.xml,v 1.13  Exp $ -\
->\n\n<Chapter><Heading>Automata <Emph>versus</Emph> rational expressions</Hea\
ding>\n\n\nA remarkable theorem due to Kleene shows that a language is recogni\
zed by a finite automaton precisely when it may be given by means of a rationa\
l expression, i.e. is a rational language.\n<P/>\nAn automaton and a rational \
expression are said to be <E>equivalent</E> when both represent the same langu\
age.\nIn this chapter we describe functions to go from automata to equivalent \
rational expressions and <E>vice-versa</E>.\n\n<Section><Heading>From automata\
 to rational expressions</Heading>\n\n\n<ManSection> \n<Func Name=\"AutomatonT\
oRatExp \" Arg=\"A\"/>\n<Func Name=\"AutToRatExp\" Arg=\"A\"/>\n<Func Name=\"F\
AtoRatExp\" Arg=\"A\"/>\n<Description>\n From a finite automaton, <C>FAtoRatEx\
p</C>, <C>AutToRatExp</C>  and <C>AutomatonToRatExp</C>, which are synonyms, c\
ompute one equivalent rational expression,\nusing the state elimination algori\
thm.\n<Example>\ngap> x:=Automaton(\"det\",4,2,[[ 0, 1, 2, 3 ],[ 0, 1, 2, 3 ]]\
,[ 3 ],[ 1, 3, 4 ]);;\ngap> FAtoRatExp(x);\n(aUb)(aUb)U@\ngap> aut:=Automaton(\
\"det\",4,\"xy\",[[ 0, 1, 2, 3 ],[ 0, 1, 2, 3 ]],[ 3 ],[ 1, 3, 4 ]);;\ngap> FA\
toRatExp(aut);\n(xUy)(xUy)U@\n</Example>\n</Description> \n</ManSection> \n</S\
ection>\n<Section><Heading>From rational expression to automata</Heading>\n\n<\
ManSection> \n<Func Name=\"RatExpToNDAut\" Arg=\"R\"/>\n<Description>\nGiven a\
 rational expression <A>R</A>, computes the equivalent NFA\n<Example>\ngap> r:\
=RationalExpression(\"aUab\");\naUab\ngap> Display(RatExpToNDAut(r));\n   |  1\
    2       3    4\n--------------------------------\n a |                   [\
 1, 2 ]\n b |      [ 3 ]\nInitial state:    [ 4 ]\nAccepting states: [ 1, 3 ]\
\ngap> r:=RationalExpression(\"xUxy\"); \nxUxy\ngap> Display(RatExpToNDAut(r))\
;    \n   |  1    2       3    4\n--------------------------------\n x |      \
             [ 1, 2 ]   \n y |      [ 3 ]                   \nInitial state:  \
  [ 4 ]\nAccepting states: [ 1, 3 ]\n</Example>\n</Description> \n</ManSection\
> \n\n<ManSection> \n<Func Name=\"RatExpToAutomaton\" Arg=\"R\"/>\n<Func Name=\
\"RatExpToAut\" Arg=\"R\"/>\n<Description>\n Given a rational expression <A>R<\
/A>, these functions, which are synonyms, use <Ref Func=\"RatExpToNDAut\"/>) t\
o compute the equivalent NFA and then returns the equivalent minimal DFA\n<Exa\
mple>\ngap> r:=RationalExpression(\"@U(aUb)(aUb)\");\n@U(aUb)(aUb)\ngap> Displ\
ay(RatExpToAut(r));\n   |  1  2  3  4\n-----------------\n a |  3  1  3  2\n b\
 |  3  1  3  2\nInitial state:    [ 4 ]\nAccepting states: [ 1, 4 ]\ngap> r:=R\
ationalExpression(\"@U(0U1)(0U1)\");\n@U(0U1)(0U1)\ngap> Display(RatExpToAut(r\
));              \n   |  1  2  3  4  \n-----------------\n 0 |  3  1  3  2  \n\
 1 |  3  1  3  2  \nInitial state:    [ 4 ]\nAccepting states: [ 1, 4 ]\n</Exa\
mple>\n</Description> \n</ManSection> \n\n</Section>\n <Section>\n    <Heading\
>\n      Some tests on automata\n    </Heading>\n    This section describes fu\
nctions that perform tests on automata, rational expressions and their accepte\
d languages.\n      <ManSection>\n        <Func Arg=\"R\" Name=\"IsEmptyLang\"\
 />\n        <Description>\n          This function tests if the language give\
n through a rational expression or an automaton\n          <Arg>\n            \
R\n          </Arg>\n          is the empty language.\n<Example>\ngap> r:=Rand\
omRatExp(2);\nempty_set\ngap> IsEmptyLang(r);\ntrue\ngap> r:=RandomRatExp(2);\
\naUb\ngap> IsEmptyLang(r);\nfalse\n</Example>\n        </Description>\n      \
</ManSection>\n      <ManSection>\n        <Func Arg=\"R\" Name=\"IsFullLang\"\
 />\n        <Description>\n          This function tests if the language give\
n through a rational expression or an automaton\n          <Arg>\n            \
R\n          </Arg>\n          represents the Kleene closure of the alphabet o\
f\n          <A>\n            R\n          </A>\n          .\n<Example>\ngap> \
r:=RationalExpression(\"aUb\");\naUb\ngap> IsFullLang(r);\nfalse\ngap> r:=Rati\
onalExpression(\"(aUb)*\");\n(aUb)*\ngap> IsFullLang(r);\ntrue\n</Example>\n  \
      </Description>\n      </ManSection>\n\n\n<ManSection> \n        <Func Ar\
g=\"A1, A2\" Name=\"AreEqualLang\" />\n<Func Name=\"AreEquivAut\" Arg=\"A1,A2 \
\"/>\n<Description>\n These functions, which are synonyms, test if the automat\
a or rational expressions <A>A1</A> and <A>A2</A> are equivalent, i.e. represe\
nt the same language. \nThis is performed by checking that the corresponding m\
inimal automata are isomorphic. Note hat this cannot happen if the alphabets a\
re different.\n<Example>\ngap> y:=RandomAutomaton(\"det\",4,2);;\ngap> x:=Rand\
omAutomaton(\"det\",4,2);;\ngap> AreEquivAut(x, y);\nfalse\ngap> a:=RationalEx\
pression(\"(aUb)*ab*\");\n(aUb)*ab*\ngap> b:=RationalExpression(\"(aUb)*\");\n\
(aUb)*\ngap> AreEqualLang(a, b);\nfalse\ngap> a:=RationalExpression(\"(bUa)*\"\
);\n(bUa)*\ngap> AreEqualLang(a, b);\ntrue\ngap> x:=RationalExpression(\"(1U0)\
*\");\n(1U0)*\ngap> AreEqualLang(a, x);  \nThe given languages are not over th\
e same alphabet\nfalse\n</Example>\n        </Description>\n      </ManSection\
>\n      <ManSection>\n        <Func Arg=\"R1, R2\" Name=\"IsContainedLang\" /\
>\n        <Description>\n          Tests if the language represented  (throug\
h an automaton or a rational expression) by\n          <A>\n            R1\n  \
        </A>\n          is contained in the language represented (through an a\
utomaton or a rational expression) by\n          <A>\n            R2\n        \
  </A>\n          .\n<Example>\ngap> r:=RationalExpression(\"aUab\");\naUab\ng\
ap> s:=RationalExpression(\"a\",\"ab\");\na\ngap> IsContainedLang(s,r);\ntrue\
\ngap> IsContainedLang(r,s);\nfalse\n</Example>\n        </Description>\n     \
 </ManSection>\n      <ManSection>\n        <Func Arg=\"R1, R2\" Name=\"AreDis\
jointLang\" />\n        <Description>\n          Tests if the languages repres\
ented (through automata or a rational expressions) by\n          <A>\n        \
    R1\n          </A>\n          and\n          <A>\n            R2\n        \
  </A>\n          are disjoint.\n<Example>\ngap> r:=RationalExpression(\"aUab\
\");;\ngap> s:=RationalExpression(\"a\",\"ab\");;\ngap> AreDisjointLang(r,s);\
\nfalse\n</Example>\n        </Description>\n      </ManSection>\n  </Section>\
\n\n</Chapter>\n\n<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<!-- $Id: aut-fu\
nc.xml,v 1.13  Exp $ -->\n\n<Chapter><Heading>Some functions involving automat\
a</Heading>\nThis chapter describes some functions involving automata. It star\
ts with functions to obtain equivalent automata of other type. Then the minima\
lization is considered.\n\n<Section><Heading>From one type to another</Heading\
>\nRecall that two automata are said to be equivalent when they recognize the \
same language.\nNext we have functions which have as input automata of one typ\
e and as output equivalent automata of another type.\n\n<ManSection> \n<Func N\
ame=\"EpsilonToNFA\" Arg=\"A\"/>\n<Description>\n<A>A</A> is an automaton with\
 <M>\\epsilon</M>-transitions. Returns a NFA\nrecognizing the same language.\n\
<Example><![CDATA[\ngap> x:=RandomAutomaton(\"epsilon\",3,2);;Display(x);\n   \
|  1          2          3\n------------------------------------\n a | [ 2 ]  \
    [ 3 ]      [ 2 ]\n b | [ 1, 2 ]   [ 1, 2 ]   [ 1, 3 ]\n @ | [ 1, 2 ]   [ 1\
, 2 ]   [ 1, 2 ]\nInitial states:   [ 2, 3 ]\nAccepting states: [ 1, 2, 3 ]\ng\
ap> Display(EpsilonToNFA(x));\n   |  1          2             3\n-------------\
-----------------------------\n a | [ 1, 2 ]   [ 1, 2, 3 ]   [ 1, 2 ]\n b | [ \
1, 2 ]   [ 1, 2 ]      [ 1, 2, 3 ]\nInitial states:   [ 1, 2, 3 ]\nAccepting s\
tates: [ 1, 2, 3 ]\n]]></Example>\n</Description> \n</ManSection> \n\n\n<ManSe\
ction> \n<Func Name=\"EpsilonToNFASet\" Arg=\"A\"/>\n<Description>\n<A>A</A> i\
s an automaton with <M>\\epsilon</M>-transitions. Returns a NFA\nrecognizing t\
he same language. This function differs from <Ref Func=\"EpsilonToNFA\"/>\nin \
that it is faster for smaller automata, or automata with few\nepsilon transiti\
ons, but slower in the really hard cases.\n</Description> \n</ManSection> \n\n\
\n\n<ManSection> \n<Func Name=\"EpsilonCompactedAut\" Arg=\"A\"/>\n<Descriptio\
n>\n<A>A</A> is an automaton with <M>\\epsilon</M>-transitions. Returns an \n<\
M>\\epsilon</M>NFA with\neach strongly-connected component of the\nepsilon-tra\
nsitions digraph of <A>A</A> identified with a single state and\nrecognizing t\
he same language.\n<Example><![CDATA[\ngap> x:=RandomAutomaton(\"epsilon\",3,2\
);;Display(x);\n   |  1          2          3\n-------------------------------\
-----\n a | [ 1, 2 ]   [ 1, 3 ]   [ 1, 2 ]\n b | [ 1, 2 ]   [ 1, 2 ]   [ 2, 3 \
]\n @ |            [ 3 ]      [ 2 ]\nInitial state:    [ 3 ]\nAccepting states\
: [ 1, 3 ]\ngap> Display(EpsilonCompactedAut(x));\n   |  1          2\n-------\
------------------\n a | [ 1, 2 ]   [ 1, 2 ]\n b | [ 1, 2 ]   [ 1, 2 ]\n @ |\n\
Initial state:    [ 2 ]\nAccepting states: [ 1, 2 ]\n]]></Example>\n</Descript\
ion> \n</ManSection> \n\n\n\n<ManSection> \n<Func Name=\"ReducedNFA\" Arg=\"A\
\"/>\n<Description>\n<A>A</A> is a non deterministic automaton (without <M>\\e\
psilon</M>-transitions). Returns an \nNFA accepting\nthe same language as its \
input but with possibly fewer states (it \nquotients out\nby the smallest righ\
t-invariant partition of the states). A paper describing\nthe algorithm is in \
preparation.\n<Example><![CDATA[\ngap> x:=RandomAutomaton(\"nondet\",5,2);;Dis\
play(x);\n   |  1             2                3             4             5\n\
----------------------------------------------------------------------\n a | [\
 1, 5 ]      [ 1, 2, 4, 5 ]   [ 1, 3, 5 ]   [ 3, 4, 5 ]   [ 4 ]\n b | [ 2, 3, \
4 ]   [ 3 ]            [ 2, 3, 4 ]   [ 2, 4, 5 ]   [ 3 ]\nInitial state:    [ \
4 ]\nAccepting states: [ 1, 3, 4, 5 ]\ngap> Display(ReducedNFA(x));\n   |  1  \
           2                3       4\n---------------------------------------\
-----------------\n a | [ 1, 3 ]      [ 1, 2, 3, 4 ]   [ 4 ]   [ 1, 3, 4 ]\n b\
 | [ 1, 2, 4 ]   [ 1 ]            [ 1 ]   [ 2, 3, 4 ]\nInitial state:    [ 4 ]\
\nAccepting states: [ 1, 3, 4 ]\n]]></Example>\n</Description> \n</ManSection>\
 \n\n\n\n<ManSection> \n<Func Name=\"NFAtoDFA\" Arg=\"A\"/>\n<Description>\nGi\
ven an NFA, these synonym functions, compute the equivalent DFA, using the pow\
erset construction,\naccording to the algorithm presented in the report of the\
 AMoRE <Cite Key=\"AMORE:95\"/> program. \nThe returned automaton is dense det\
erministic\n<Example><![CDATA[\ngap> x:=RandomAutomaton(\"nondet\",3,2);;Displ\
ay(x);\n   |  1       2    3\n---------------------------\n a | [ 2 ]        [\
 1, 3 ]\n b |              [ 2, 3 ]\nInitial states:   [ 1, 3 ]\nAccepting sta\
tes: [ 1, 2 ]\ngap> Display(NFAtoDFA(x));\n   |  1  2  3\n--------------\n a |\
  2  2  1\n b |  3  3  3\nInitial state:    [ 1 ]\nAccepting states: [ 1, 2, 3\
 ]\n]]></Example>\n</Description> \n</ManSection> \n\n\n<ManSection> \n<Func N\
ame=\"FuseSymbolsAut\" Arg=\"A, s1, s2\"/>\n<Description>\nGiven an automaton \
<A>A</A> and integers <A>s1</A> and <A>s2</A> which, returns an NFA\nobtained \
by replacing all transitions through <A>s2</A> by transitions through <A>s1</A\
>.\n<Example><![CDATA[\ngap> x:=RandomAutomaton(\"det\",3,2);;Display(x);\n   \
|  1  2  3\n--------------\n a |  2  3\n b |     1\nInitial state:    [ 3 ]\nA\
ccepting states: [ 1, 2, 3 ]\ngap> Display(FuseSymbolsAut(x,1,2));\n   |  1   \
    2          3\n---------------------------\n a | [ 2 ]   [ 1, 3 ]\nInitial \
state:    [ 3 ]\nAccepting states: [ 1, 2, 3 ]\n]]></Example>\n</Description> \
\n</ManSection> \n\n\n\n</Section>\n\n\n<Section><Heading>Minimalization of an\
 automaton</Heading>\nThe algorithm used to minimalize a dense deterministic a\
utomaton (i.e., to\ncompute a dense minimal \nautomaton recognizing the same l\
anguage) is based on an algorithm due to\nHopcroft (see <Cite Key=\"AHU:74\"/>\
). It is well known (see <Cite Key=\"HU:69\"/>) that it suffices\nto reduce th\
e automaton given and remove the inaccessible states. Again, the\ndocumentatio\
n for the computer program AMoRE <Cite Key=\"AMORE:95\"/> has been very useful\
.\n\n<ManSection> \n<Func Name=\"UsefulAutomaton\" Arg=\"A\"/>\n<Description>\
\nGiven an automaton <A>A</A> (deterministic or not), outputs a dense DFA <A>B\
</A> whose states are all reachable and such that <A>A</A> and <A>B</A> are eq\
uivalent.\n<Example><![CDATA[\ngap> x:=RandomAutomaton(\"det\",4,2);;Display(x\
);\n   |  1  2  3  4\n-----------------\n a |     3  4\n b |  1  4\nInitial st\
ate:    [ 3 ]\nAccepting states: [ 2, 3, 4 ]\ngap> Display(UsefulAutomaton(x))\
;\n   |  1  2  3\n--------------\n a |  2  3  3\n b |  3  3  3\nInitial state:\
    [ 1 ]\nAccepting states: [ 1, 2 ]\n]]></Example>\n</Description> \n</ManSe\
ction> \n\n<ManSection> \n<Func Name=\"MinimalizedAut\" Arg=\"A\"/>\n<Descript\
ion>\nReturns the minimal automaton equivalent to <A>A</A>.\n<Example><![CDATA\
[\ngap> x:=RandomAutomaton(\"det\",4,2);;Display(x);\n   |  1  2  3  4\n------\
-----------\n a |     3  4\n b |  1  2  3\nInitial state:    [ 4 ]\nAccepting \
states: [ 2, 3, 4 ]\ngap> Display(MinimalizedAut(x));\n   |  1  2\n-----------\
\n a |  2  2\n b |  2  2\nInitial state:   [ 1 ]\nAccepting state: [ 1 ]\n]]><\
/Example>\n</Description> \n</ManSection> \n\n<ManSection> \n<Attr Name=\" Min\
imalAutomaton\" Arg=\"A\"/>\n<Description>\nReturns the minimal automaton equi\
valent to <A>A</A>, but stores it so that\nfuture computations of this automat\
on just return the stored automaton.\n<Example><![CDATA[\ngap> x:=RandomAutoma\
ton(\"det\",4,2);;Display(x);\n   |  1  2  3  4\n-----------------\n a |     2\
  4\n b |     3  4\nInitial state:    [ 4 ]\nAccepting states: [ 1, 2, 3 ]\nga\
p> Display(MinimalAutomaton(x));\n   |  1\n--------\n a |  1\n b |  1\nInitial\
 state:   [ 1 ]\nAccepting state:\n]]></Example>\n</Description> \n</ManSectio\
n> \n\n<ManSection> \n<Func Name=\"AccessibleStates\" Arg=\"aut [, p]\"/>\n<De\
scription>\nComputes the list of states of the automaton <A>aut</A> \n which a\
re accessible from state <A>p</A>. When <A>p</A> is not given, returns the sta\
tes which are accessible from any initial state.\n<Example><![CDATA[\ngap> x:=\
RandomAutomaton(\"det\",4,2);;Display(x);\n   |  1  2  3  4\n-----------------\
\n a |     1  2  4\n b |     2  4\nInitial state:    [ 2 ]\nAccepting states: \
[ 1, 2, 3 ]\ngap> AccessibleStates(x,3);\n[ 1, 2, 3, 4 ]\n]]></Example>\n</Des\
cription> \n</ManSection> \n\n<ManSection> \n<Func Name=\"AccessibleAutomaton\
\" Arg=\"A\"/>\n<Description>\n If  <A>A</A> is a deterministic automaton, not\
 necessarily dense, an \n equivalent dense deterministic accessible automaton \
is returned. \n (The function <C>UsefulAutomaton</C> is called.)\n<P/>\n If  <\
A>A</A> is not deterministic with a single initial state, an equivalent \n acc\
essible automaton is returned.\n\n<Example><![CDATA[\ngap> x:=RandomAutomaton(\
\"det\",4,2);;Display(x);\n   |  1  2  3  4\n-----------------\n a |  1  3\n b\
 |  1  3  4\nInitial state:    [ 2 ]\nAccepting states: [ 3, 4 ]\ngap> Display\
(AccessibleAutomaton(x));\n   |  1  2  3  4\n-----------------\n a |  2  4  4 \
 4\n b |  2  3  4  4\nInitial state:    [ 1 ]\nAccepting states: [ 2, 3 ]\n]]>\
</Example>\n</Description> \n</ManSection> \n\n<ManSection> \n<Func Name=\"Int\
ersectionLanguage\" Arg=\"A1,A2\"/>\n<Func Name=\"IntersectionAutomaton\" Arg=\
\"A1,A2\"/>\n<Description>\nComputes an automaton that recognizes the intersec\
tion of the languages given (through automata or rational expressions by) <A>A\
1</A> and <A>A2</A>.\nWhen the arguments are deterministic automata, is the sa\
me as ProductAutomaton, but works for all kinds of automata. Note that the lan\
guage of the product of two automata is precisely the intersection of the lang\
uages of the automata.\n<Example><![CDATA[\ngap> x:=RandomAutomaton(\"det\",3,\
2);;Display(x);\n   |  1  2  3\n--------------\n a |  2  3\n b |     1\nInitia\
l state:    [ 3 ]\nAccepting states: [ 1, 2, 3 ]\ngap> y:=RandomAutomaton(\"de\
t\",3,2);;Display(y);\n   |  1  2  3\n--------------\n a |     1\n b |  1  3\n\
Initial state:    [ 3 ]\nAccepting states: [ 1, 3 ]\ngap> Display(Intersection\
Language(x,y));\n   |  1  2\n-----------\n a |  2  2\n b |  2  2\nInitial stat\
e:   [ 1 ]\nAccepting state: [ 1 ]\n]]></Example>\n</Description> \n</ManSecti\
on> \n\n\n<ManSection> \n<Func Name=\"AutomatonAllPairsPaths\" Arg=\"A\"/>\n<D\
escription>\nGiven an automaton <A>A</A>, with <C>n</C> states, outputs a <C>n\
</C> x <C>n</C> matrix P,\nsuch that P[i][j] is the list of simple paths from \
state i to\nstate j in <A>A</A>.\n<Example><![CDATA[\ngap> a:=RandomAutomaton(\
\"det\",3,2);\n< deterministic automaton on 2 letters with 3 states >\ngap> Au\
tomatonAllPairsPaths(a);\n[ [ [ [ 1, 1 ] ], [  ], [  ] ], [ [ [ 2, 1 ] ], [ [ \
2, 2 ] ], [  ] ],\n  [ [ [ 3, 2, 1 ] ], [ [ 3, 2 ] ], [ [ 3, 3 ] ] ] ]\ngap> D\
isplay(a);\n   |  1  2  3\n--------------\n a |     1  2\n b |  1  2  3\nIniti\
al state:    [ 3 ]\nAccepting states: [ 1, 2 ]\n]]></Example>\n</Description> \
\n</ManSection> \n\n\n    </Section>\n</Chapter>\n\n\n\n\n\n<?xml version=\"1.\
0\" encoding=\"UTF-8\"?>\n<!-- $Id: finitelang.xml,v 1.13  Exp $ -->\n\n<Chapt\
er><Heading>Finite regular languages</Heading>\nThis chapter describes some fu\
nctions to deal with finite regular languages.\n\n<Section><Heading>Dealing wi\
th finite regular languages</Heading>\n\n<ManSection> \n<Func Name=\"IsFiniteR\
egularLanguage\" Arg=\"L\"/>\n<Description>\n<A>L</A> is an automaton or a rat\
ional expression. This function tests\nwhether its argument represents a finit\
e language or not.\n<Example><![CDATA[\ngap> RandomRatExp(2);\nb*(aU@)\ngap> I\
sFiniteRegularLanguage(last);\nfalse\ngap> RandomRatExp(2);\naUbU@\ngap> IsFin\
iteRegularLanguage(last);\ntrue\n]]></Example>\n</Description> \n</ManSection>\
 \n\n\n<ManSection> \n<Func Name=\"FiniteRegularLanguageToListOfWords\" Arg=\"\
L\"/>\n<Description>\n<A>L</A> is an automaton or a rational expression. \nThi\
s function outputs the recognized language as a list of words.\n<Example><![CD\
ATA[\ngap> r:=RationalExpression(\"aaUx(aUb)\");   \naaUx(aUb)\ngap>  FiniteRe\
gularLanguageToListOfWords(r);\n[ \"aa\", \"xa\", \"xb\" ]\n]]></Example>\n</D\
escription> \n</ManSection> \n\n\n<ManSection> \n<Func Name=\"ListOfWordsToAut\
omaton\" Arg=\"alph, L\"/>\n<Description>\nGiven an alphabet <A>alph</A> (a li\
st) and a list of\nwords <A>L</A> (a list of lists), outputs an automaton\ntha\
t recognizes the given list of words.\n<Example><![CDATA[\ngap> ListOfWordsToA\
utomaton(\"ab\",[\"aaa\",\"bba\",\"\"]);\n< deterministic automaton on 2 lette\
rs with 6 states >\ngap> FAtoRatExp(last);\n(bbUaa)aU@\n]]></Example>\n</Descr\
iption> \n</ManSection> \n\n\n\n\n\n    </Section>\n</Chapter>\n\n\n\n\n\n\n</\
Body>\n\n<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<!-- $Id: graphs.xml,v 1.\
13  Exp $ -->\n<Appendix><Heading>Directed graphs</Heading>\nAutomata are freq\
uently described through directed labeled graphs. This appendix on directed gr\
aphs (digraphs) is devoted to some functions designed with the purpose of bein\
g used as auxiliary functions to deal with automata, but may have independent \
interest.\n\n\n<Section><Heading>Directed graphs</Heading>\nA directed graph w\
ith <M>n</M> vertices is represented by an adjacency list.\n\nFor example, the\
 list <C>G = [[2,4],[3],[1,4],[]]</C> represents a directed graph with <C>4 (=\
 Length(G))</C> vertices; the sublist in position <C>i</C> is the list of endp\
oints of the edges beginning in vertex <M>i</M>.\n    <Alt Only=\"LaTeX\">\n  \
    \\begin{figure}[htbp] \\begin{center} \\leavevmode \\includegraphics[bb=0 \
0 132 299]{graph} \\end{center} \\label{fig:graph} \\end{figure}\n    </Alt>\n\
    <Alt Only=\"HTML\">\n      &#60;br&#62;&#60;center&#62;&#60;img src=&#34;g\
raph.gif&#34;&#62;&#60;/center&#62;&#60;br&#62;\n    </Alt>\n    <P />\n\n<Man\
Section> \n<Func Name=\"RandomDiGraph\" Arg=\"n\"/>\n<Description>\nProduces a\
 pseudo random digraph with <M>n</M> vertices\n<Example><![CDATA[\ngap> Random\
DiGraph(4);\n[ [  ], [ 1, 2, 4 ], [  ], [  ] ]\n]]></Example>\n</Description> \
\n</ManSection> \n\n\n<ManSection> \n<Func Name=\"VertexInDegree\" Arg=\"DG,v\
\"/>\n<Description>\nComputes the in degree of the vertex <A>v</A> of the dire\
cted graph <A>DG</A>\n<Example><![CDATA[\ngap> G:=RandomDiGraph(4);\n[ [ 1 ], \
[ 1, 2, 4 ], [  ], [ 1, 2, 3 ] ]\ngap> VertexInDegree(G,2);\n2\n]]></Example>\
\n</Description> \n</ManSection> \n\n\n<ManSection> \n<Func Name=\"VertexOutDe\
gree\" Arg=\"DG,v\"/>\n<Description>\nComputes the out degree of the vertex <A\
>v</A> of the directed graph <A>DG</A>\n<Example><![CDATA[\ngap> G:=RandomDiGr\
aph(4);\n[ [ 1 ], [ 1, 2, 4 ], [  ], [ 1, 2, 3 ] ]\ngap> VertexOutDegree(G,2);\
\n3\n]]></Example>\n</Description> \n</ManSection> \n\n\n<ManSection> \n<Func \
Name=\"AutoVertexDegree\" Arg=\"DG,v\"/>\n<Description>\nComputes the degree o\
f the vertex <A>v</A> of the directed graph <A>DG</A>\n<Example><![CDATA[\ngap\
> G:=RandomDiGraph(4);\n[ [ 1 ], [ 1, 2, 4 ], [  ], [ 1, 2, 3 ] ]\ngap> AutoVe\
rtexDegree(G,2);\n5\n]]></Example>\n</Description> \n</ManSection> \n\n\n\n\n<\
ManSection> \n<Func Name=\"ReversedGraph\" Arg=\"G\"/>\n<Description>\nCompute\
s the reversed graph of the directed graph G. It is the graph \nobtained from \
G by reversing the edges.\n<Example><![CDATA[\ngap> G:=RandomDiGraph(4);\n[ [ \
 ], [ 4 ], [ 2 ], [ 1, 4 ] ]\ngap> ReversedGraph(G);\n[ [ 4 ], [ 3 ], [  ], [ \
2, 4 ] ]\n]]></Example>\n</Description> \n</ManSection> \n\nWe say that a digr\
aph is connected when for every pair of vertices there \nis a path consisting \
of directed or reversed edges from one vertex to \nthe other.\n\n<ManSection> \
\n<Func Name=\"AutoConnectedComponents\" Arg=\"G\"/>\n<Description>\nComputes \
a list of the connected components of the digraph\n\n<Example><![CDATA[\ngap> \
G:=RandomDiGraph(6);\n[ [  ], [ 1, 4, 5, 6 ], [  ], [ 1, 3, 5, 6 ], [ 2, 3 ], \
[ 2, 4, 6 ] ]\ngap> AutoConnectedComponents(G);\n[ [ 1, 2, 3, 4, 5, 6 ] ]\n]]>\
</Example>\n</Description> \n\n</ManSection> \n\nTwo vertices of a digraph bel\
ong to a strongly connected component if there is a directed path from each on\
e to the other.<P/>\n\n<ManSection> \n<Func Name=\"GraphStronglyConnectedCompo\
nents\" Arg=\"G\"/>\n<Description>\nProduces the strongly connected components\
 of the digraph <A>G</A>. \n<Example><![CDATA[\ngap> G:=RandomDiGraph(6);\n[ [\
  ], [ 4 ], [  ], [ 4, 6 ], [  ], [ 1, 4, 5, 6 ] ]\ngap> GraphStronglyConnecte\
dComponents(G);\n[ [ 1 ], [ 2 ], [ 3 ], [ 4, 6 ], [ 5 ] ]\n]]></Example>\n</De\
scription> \n</ManSection> \n\n<ManSection> \n<Func Name=\"UnderlyingMultiGrap\
hOfAutomaton\" Arg=\"A \"/>\n<Description>\n<A>A</A> is an automaton. The outp\
ut is the underlying directed multi-graph.\n<Example><![CDATA[\ngap> a:=Random\
Automaton(\"det\",3,2);;Display(a);\n   |  1  2  3\n--------------\n a |  1  3\
\n b |     2  3\nInitial state:    [ 1 ]\nAccepting states: [ 1, 2 ]\ngap> Und\
erlyingMultiGraphOfAutomaton(a);\n[ [ 1 ], [ 3, 2 ], [ 3 ] ]\n]]></Example>\n<\
/Description> \n</ManSection> \n\n<ManSection> \n<Func Name=\"UnderlyingGraphO\
fAutomaton\" Arg=\"A\"/>\n<Description>\n<A>A</A> is an automaton. The output \
is the underlying directed graph.\n<Example><![CDATA[\ngap> a:=RandomAutomaton\
(\"det\",3,2);;Display(a);\n   |  1  2  3\n--------------\n a |     1  2\n b |\
  1  2\nInitial state:   [ 2 ]\nAccepting state: [ 2 ]\ngap> UnderlyingGraphOf\
Automaton(a);\n[ [ 1 ], [ 1, 2 ], [ 2 ] ]\n]]></Example>\n</Description> \n</M\
anSection> \n\n<ManSection> \n<Func Name=\"DiGraphToRelation\" Arg=\"D\"/>\n<D\
escription>\nReturns the relation corresponding to the digraph. Note that a di\
rected graph may be seen in a natural way as a binary relation on the set of v\
ertices.\n<Example><![CDATA[\ngap> G:=RandomDiGraph(4);\n[ [  ], [  ], [ 4 ], \
[ 4 ] ]\ngap> DiGraphToRelation(G);\n[ [ 3, 4 ], [ 4, 4 ] ]\n]]></Example>\n</\
Description> \n</ManSection> \n\n<ManSection> \n<Func Name=\"MSccAutomaton\" A\
rg=\"A\"/>\n<Description>\nProduces an automaton where, in each strongly conne\
cted component,\nedges labeled by inverses are added. (M stands for modified.)\
\n<P/>\nThis construction is useful in Finite Semigroup Theory.\n<Example><![C\
DATA[\ngap> a:=RandomAutomaton(\"det\",3,2);;Display(a);\n   |  1  2  3\n-----\
---------\n a |  1  3\n b |  2  3\nInitial state:    [ 1 ]\nAccepting states: \
[ 1, 2, 3 ]\ngap> MSccAutomaton(a);\n< deterministic automaton on 4 letters wi\
th 3 states >\ngap> Display(last);\n   |  1  2  3\n--------------\n a |  1  3\
\n b |  2  3\n A |  1\n B |\nInitial state:    [ 1 ]\nAccepting states: [ 1, 2\
, 3 ]\n]]></Example>\n</Description> \n</ManSection> \n\n\n<ManSection> \n<Fun\
c Name=\"AutoIsAcyclicGraph\" Arg=\"G\"/>\n<Description>\nThe argument is a gr\
aph's list of adjacencies\nand this function returns true if the argument\nis \
an acyclic graph and false otherwise.\n<Example><![CDATA[\ngap> RandomDiGraph(\
3);\n[ [  ], [ 3 ], [ 2 ] ]\ngap> AutoIsAcyclicGraph(last);\nfalse\n]]></Examp\
le>\n</Description> \n</ManSection> \n\n\n</Section>\n</Appendix>\n\n\n<?xml v\
ersion=\"1.0\" encoding=\"UTF-8\"?>\n  <!-- $Id: drawing.xml,v 1.13  Exp $ -->\
\n  <Appendix>\n    <Heading>\n      Drawing automata\n    </Heading>\n    The\
 drawing of graphs described here uses\n    <C>graphviz</C> <Cite Key=\"Koutso\
fiosNorth:2002\"/>, a software for drawing graphs developed at AT\n    <Alt On\
ly=\"LaTeX\">\n      \\&#38;\n    </Alt>\n    <Alt Not=\"LaTeX\">\n      <Alt \
Only=\"HTML\">\n        &#38;amp;\n      </Alt>\n      <Alt Not=\"HTML\">\n   \
     &#38;\n      </Alt>\n    </Alt>\n    T Labs, that can be obtained at\n   \
 <URL>http://www.graphviz.org/</URL>.\n    <Section>\n      <Heading>\n       \
 Installing some external programs\n      </Heading>\n      In order to create\
 the drawings you should install <URL Text=\"graphviz\">http://www.graphviz.or\
g/</URL>\n      and to view them you should install one of <URL Text=\"evince\
\">http://www.gnome.org/projects/evince/</URL>,\n      <URL Text=\"ggv\">http:\
//directory.fsf.org/GNU/ggv.html</URL>,\n      <URL Text=\"gsview\">http://pag\
es.cs.wisc.edu/~ghost/gsview/</URL> or\n      <URL Text=\"gv\">http://www.gnu.\
org/software/gv/</URL>.\n    </Section>\n    <Section>\n      <Heading>\n     \
   Functions to draw automata\n      </Heading>\n      <ManSection>\n        <\
Func Arg=\"A [,state_names, L, file]\" Name=\"DrawAutomaton\" />\n        <Des\
cription>\n          This function draws automaton\n          <A>A</A>.\n\t  T\
he arguments <A>state_names</A>, <A>L</A> and <A>file</A> are optional.\n\n\t \
 <P />\n\t  An automaton with <C>n</C> states will be drawn with numbers <C>1<\
/C> to <C>n</C>\n\t  written inside the corresponding graph node.\n\t  The arg\
ument <A>state_names</A> is a list of <C>n</C> strings which will be the new t\
ext\n\t  written inside the corresponding graph node.\n\n\t  <P />\n\t  The ar\
gument <A>L</A> is a list of lists of integers, each of which specifies a set\
\n\t  of states to be drawn in a different color.\n\n\t  <P />\n\t  The argume\
nt <A>file</A> is a string that specifies the name of the file containing the \
drawing.\n\t  If it is not give, it defaults to <C>\"automaton\"</C>.\n<Exampl\
e><![CDATA[\ngap> x:=Automaton(\"det\",3,2,[ [ 2, 3, 0 ], [ 0, 1, 2 ] ],[ 1 ],\
[ 1, 2, 3 ]);;\ngap> DrawAutomaton(x,\"file_name\");\nDisplaying file: /tmp/tm\
p.Rj0v1s/file_name.dot.ps\n\ngap> DrawAutomaton(x,[\"st 1\", \"2\", \"C\"],\"f\
ile_name\");\nDisplaying file: /tmp/tmp.BCH3FO/file_name.dot.ps\n\ngap> DrawAu\
tomaton(x,[\"st 1\", \"2\", \"C\"],[[2],[1,3]]);\nDisplaying file: /tmp/tmp.LP\
nJMq/automaton.dot.ps\n]]></Example>\nThe output of the three previous <C>Draw\
Automaton</C> commands would be the following diagrams displayed in a <E>ghost\
view</E> window,\nrespectively.\n<P />\n    <Alt Only=\"LaTeX\">\n      \\begi\
n{figure}[htbp] \\begin{center} \\leavevmode \\includegraphics[bb=0 0 74 250]{\
aut2.jpg} \\end{center} \\label{fig:aut2} \\end{figure}\n    </Alt>\n    <Alt \
Only=\"HTML\">\n      &#60;br&#62;&#60;center&#62;&#60;img src=&#34;aut2.jpg&#\
34;&#62;&#60;/center&#62;&#60;br&#62;\n    </Alt>\n    <P />\n    <Alt Only=\"\
LaTeX\">\n      \\begin{figure}[htbp] \\begin{center} \\leavevmode \\includegr\
aphics[bb=0 0 100 250]{aut2_1.jpg} \\end{center} \\label{fig:aut2_1} \\end{fig\
ure}\n    </Alt>\n    <Alt Only=\"HTML\">\n      &#60;br&#62;&#60;center&#62;&\
#60;img src=&#34;aut2_1.jpg&#34;&#62;&#60;/center&#62;&#60;br&#62;\n    </Alt>\
\n    <P />\n    <Alt Only=\"LaTeX\">\n      \\begin{figure}[htbp] \\begin{cen\
ter} \\leavevmode \\includegraphics[bb=0 0 100 250]{aut2_2.jpg} \\end{center} \
\\label{fig:aut2_2} \\end{figure}\n    </Alt>\n    <Alt Only=\"HTML\">\n      \
&#60;br&#62;&#60;center&#62;&#60;img src=&#34;aut2_2.jpg&#34;&#62;&#60;/center\
&#62;&#60;br&#62;\n    </Alt>\n    <P />\n        </Description>\n      </ManS\
ection>\n      <ManSection>\n        <Func Arg=\"A, B [, file]\" Name=\"DrawAu\
tomata\" />\n        <Description>\n          This function tests if automaton\
\n          <C>\n            A\n          </C>\n          is a subautomaton of\
\n          <C>\n            B\n          </C>\n          in which case draws\
\n          <C>\n            B\n          </C>\n          highlighting the edg\
es not in\n          <C>\n            A\n          </C>\n          by drawing \
them in a dotted style, while the others are drawn in a plain style.\n        \
</Description>\n      </ManSection>\n      <ManSection>\n        <Func Arg=\"G\
 [, file]\" Name=\"DrawGraph\" />\n        <Description>\n          Draws a gr\
aph specified as an adjacency list\n          <C>G</C>.\n        </Description\
>\n      </ManSection>\n      <ManSection>\n        <Func Arg=\"A [,state_name\
s, L, file]\" Name=\"DrawSCCAutomaton\" />\n        <Description>\n          D\
raws automaton\n          <C>\n            A\n          </C>\n          and hi\
ghlights it&#39;s strongly connected components by drawing the other edges in \
a dotted style.\n\t  <P />\n\t  The optional arguments <A>state_names</A>, <A>\
L</A> and <A>file</A> are as described in\n\t  <Ref Func=\"DrawAutomaton\" />.\
\n        </Description>\n      </ManSection>\n    </Section>\n\n    <Section>\
\n       <Heading>Drawings output formats</Heading>\n       Since drawings are\
 mostly used in the <Package>SgpViz</Package> package, please\n       refer to\
 that package's\n       <URL Text=\"manual\">http://www.gap-system.org/Manuals\
/pkg/sgpviz/doc/manual.html</URL>\n       section of the same name.\n    </Sec\
tion>\n    \n    <Section>\n            <Heading>Drawings extra graph attribut\
es</Heading>\n       Since drawings are mostly used in the <Package>SgpViz</Pa\
ckage> package, please\n       refer to that package's\n       <URL Text=\"man\
ual\">http://www.gap-system.org/Manuals/pkg/sgpviz/doc/manual.html</URL>\n    \
   section of the same name.\n    </Section>\n  </Appendix>\n\n<?xml version=\
\"1.0\" encoding=\"UTF-8\"?>\n<!-- $Id: foldings.xml,v 1.13  Exp $ -->\n\n<App\
endix><Heading>Inverse automata and subgroups of the free group</Heading>\n\nI\
nverse automata with a single initial/accepting state are in a one to one corr\
espondence with finitely generated subgroups of the free group over the alphab\
et of the automaton. See  <Cite Key=\"MSW:2001\"/>, <Cite Key=\"KM:2002\" /> f\
or details, as well as for concepts such as <E>flower automaton</E> and <E>Sta\
llings foldings</E>.\n\n\n<Section><Heading>From subgroups to inverse automata\
</Heading>\n\nA finitely generated subgroup of a finitely generated free group\
 is given\nthrough a list whose first element is the number of generators of t\
he \nfree group and the remaining elements are the generators of the subgroup.\
\nThe set of generators of the free group of rank <M>n</M> consists on the <M>\
n</M> first letters of the set <M>\\{a,b,c,d,e,f,g\\}</M>. In particular, free\
 groups of rank greater than <M>8</M> must not be considered. A formal inverse\
 of a generator is represented by the corresponding capital letter.\n<P/>\nA g\
enerator of the subgroup may be given through a string of letters or \nthrough\
 a list of positive integers as should be clear from the example that follows.\
 \n<P/>\nFor example, <C>[2,\"abA\",\"bbabAB\"]</C> stands for the subgroup of\
 the free group of rank 2\non the generators <M>aba^{-1}</M> and <M>bbaba^{-1}\
b^{-1}</M>.\nThe same subgroup may be given as <C>[2,[1,2,3],[2,2,1,2,3,4]]</C\
>. The number <M> n+j</M> represents the formal inverse of the generator repre\
sented by <M>j</M>. One can go from one representation to another, using the f\
ollowing functions.\n\n<ManSection> \n<Func Name=\"GeneratorsToListRepresentat\
ion\" Arg=\"L\"/>\n<Description> \n<Example><![CDATA[\ngap> L:=[2,\"abA\",\"bb\
abAB\"];;\ngap> GeneratorsToListRepresentation(L);\n[ 2, [ 1, 2, 3 ], [ 2, 2, \
1, 2, 3, 4 ] ]\n]]></Example>\n</Description> \n</ManSection> \n\n\n<ManSectio\
n> \n<Func Name=\"ListToGeneratorsRepresentation\" Arg=\"K\"/>\n<Description>\
\n<Example><![CDATA[\ngap> K:=[2,[1,2,3],[2,2,1,2,3,4]];;\ngap> ListToGenerato\
rsRepresentation(K);\n[ 2, \"abA\", \"bbabAB\" ]\n]]></Example>\n</Description\
> </ManSection> \n\n<ManSection> \n<Func Name=\"FlowerAutomaton\" Arg=\"L\"/>\
\n<Description>\nThe argument <C>L</C> is a subgroup of the free group given t\
hrough any \nof the representations described above. Returns the flower automa\
ton.\n<Example><![CDATA[\ngap> W:=[2,\"bbbAB\",\"abAbA\"];;\ngap> A:=FlowerAut\
omaton(W);\n< non deterministic automaton on 2 letters with 9 states >\ngap> D\
isplay(A);\n   |  1          2       3       4    5       6       7    8      \
 9\n---------------------------------------------------------------------\n a \
| [ 6, 9 ]                        [ 4 ]                [ 7 ]\n b | [ 2, 5 ]   \
[ 3 ]   [ 4 ]                [ 7 ]        [ 9 ]\nInitial state:   [ 1 ]\nAccep\
ting state: [ 1 ]\n]]></Example>\n</Description> </ManSection> \n\n<ManSection\
> \n<Func Name=\"FoldFlowerAutomaton\" Arg=\"A\"/>\n<Description>\n Makes iden\
tifications on the flower automaton <C>A</C>. In the literature, these identif\
ications are called Stallings foldings.\n<P/>\n(This function may have <C>true\
</C> as a second argument. WARNING: the second argument should only be used wh\
en facilities to draw automata are available. In that case, one may visualize \
the identifications that are taking place.)\n<Example><![CDATA[\ngap> B := Fol\
dFlowerAutomaton(A);\n< deterministic automaton on 2 letters with 7 states >\n\
gap> Display(B);\n   |  1  2  3  4  5  6  7\n--------------------------\n a | \
 5  4              6\n b |  2  3  4     6     5\nInitial state:   [ 1 ]\nAccep\
ting state: [ 1 ]\n]]></Example>\n</Description> </ManSection>\n<ManSection>\n\
 <Func Name=\"SubgroupGenToInvAut\" Arg=\"L\"/>\n<Description>\nReturns the in\
verse automaton corresponding to the subgroup given by \n<A>L</A>.\n<Example><\
![CDATA[\ngap> L:=[2,\"bbbAB\",\"AbAbA\"];;\ngap> SubgroupGenToInvAut(L);\n< d\
eterministic automaton on 2 letters with 8 states >\ngap> Display(last);\n   |\
  1  2  3  4  5  6  7  8\n-----------------------------\n a |  8  4        1  \
   6\n b |  2  3  4     6     8\nInitial state:   [ 1 ]\nAccepting state: [ 1 \
]\n\n]]></Example>\n</Description> </ManSection>\n</Section>\n<Section><Headin\
g>From inverse automata to subgroups</Heading>\nGiven an inverse automaton wit\
h a single initial/accepting state, one can find a set of generators for the s\
ubgroup represented by the automaton. Moreover, using a geodesic tree, one can\
 find a Nielsen reduced set of generators <Cite Key=\"KM:2002\" />.\n\n<ManSec\
tion> \n<Func Name=\"GeodesicTreeOfInverseAutomaton\" Arg=\"A\"/>\n<Descriptio\
n>\nReturns a subautomaton of <A>A</A>whose underlying graph is a geodesic tre\
e of the underlying graph of the inverse automaton <C>A</C>.  \n<Example><![CD\
ATA[\ngap> A:=Automaton(\"det\",4,2,[ [ 3, 4, 0, 0 ], [ 2, 3, 4, 0 ] ],[ 1 ],[\
 1 ]);;\ngap> G := GeodesicTreeOfInverseAutomaton(A);\n< deterministic automat\
on on 2 letters with 4 states >\ngap> Display(G);\n   |  1  2  3  4\n---------\
--------\n a |  3\n b |  2     4\nInitial state:   [ 1 ]\nAccepting state: [ 1\
 ]\n]]></Example>\n</Description> \n</ManSection> \n\n<ManSection> \n<Func Nam\
e=\"InverseAutomatonToGenerators\" Arg=\"A\"/>\n<Description>\nReturns a set o\
f generators (given trough the representation above) of the \nsubgroup of the \
free group corresponding to the automaton <C>A</C> given.\n<Example><![CDATA[\
\ngap> NW := InverseAutomatonToGenerators(A);\n[ 2, \"baBA\", \"bbA\" ]\n]]></\
Example>\n</Description> \n</ManSection> \n\n</Section>\n</Appendix>\n\n\n\n\n\
\n<Bibliography Databases=\"AutMan\" />\n\n<TheIndex/>\n\n</Book>\n\n<!-- ====\
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  sixindex := [ 1, 2, 4, 3, 5, 6, 7, 8, 40, 41, 42, 43, 44, 45, 46, 9, 47, 
      48, 49, 50, 51, 52, 53, 54, 10, 11, 55, 56, 57, 58, 59, 60, 12, 61, 62, 
      63, 64, 65, 66, 67, 68, 69, 70, 71, 13, 72, 73, 74, 75, 14, 15, 76, 77, 
      78, 79, 80, 81, 82, 83, 16, 17, 84, 85, 86, 18, 19, 87, 88, 89, 20, 90, 
      92, 91, 21, 93, 94, 96, 95, 97, 98, 22, 23, 99, 100, 101, 102, 103, 
      104, 24, 105, 106, 107, 108, 109, 110, 111, 112, 25, 26, 113, 114, 115, 
      27, 28, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 29, 
      30, 31, 128, 129, 130, 131, 32, 33, 38, 37, 34, 35, 132, 133, 134, 135, 
      136, 36, 137, 138, 39 ], start := 0, stop := 73961, 
  toctext := "<div class=\"ContChap\"><a href=\"chap1_mj.html#X7DFB63A97E67C0A\
1\">1 <span class=\"Heading\">\n      Introduction\n    </span></a>\n</div>\n<\
div class=\"ContChap\"><a href=\"chap2_mj.html#X811E5FC2849C5644\">2 <span cla\
ss=\"Heading\">Finite Automata</span></a>\n<div class=\"ContSect\"><span class\
=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap2_mj.html#X821C3\
B3687B1F2FF\">2.1 <span class=\"Heading\">Automata generation</span></a>\n</sp\
an>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X87D8222D7B50731E\">2.1-1 Au\
tomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap2_mj.html#X83CCDEF9814F1E6D\">2.1-2 IsAutomaton</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap2_mj.html#X7D39CECC7E12DD8A\">2.1-3 IsDeterministicAutomaton</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap2_mj.html#X83C1148481BAA3DD\">2.1-4 IsNonDeterministicAutomaton\
</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</\
span><a href=\"chap2_mj.html#X81EC5331790D6022\">2.1-5 IsEpsilonAutomaton</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap2_mj.html#X81FB5BE27903EC32\">2.1-6 String</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_m\
j.html#X801019097C93BCCC\">2.1-7 RandomAutomaton</a></span>\n</div></div>\n<di\
v class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</spa\
n><a href=\"chap2_mj.html#X80AB906D86BBC153\">2.2 <span class=\"Heading\">Auto\
mata internals</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.h\
tml#X7A34B47778B50FFE\">2.2-1 AlphabetOfAutomaton</a></span>\n<span class=\"Co\
ntSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#\
X8044B24B82C59BBF\">2.2-2 AlphabetOfAutomatonAsList</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.htm\
l#X872BB42A81E4D0E7\">2.2-3 TransitionMatrixOfAutomaton</a></span>\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj\
.html#X7B5C3CFA83FF80EA\">2.2-4 InitialStatesOfAutomaton</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_m\
j.html#X8408FE8487028B7F\">2.2-5 SetInitialStatesOfAutomaton</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p2_mj.html#X78CDDCC27D085F00\">2.2-6 FinalStatesOfAutomaton</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
2_mj.html#X80689F1480F9D959\">2.2-7 SetFinalStatesOfAutomaton</a></span>\n<spa\
n class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"ch\
ap2_mj.html#X7D22AD207A3D5FF4\">2.2-8 NumberStatesOfAutomaton</a></span>\n</di\
v></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\
\">&nbsp;</span><a href=\"chap2_mj.html#X8454E24E7D9FC1C2\">2.3 <span class=\"\
Heading\">Comparison of automata</span></a>\n</span>\n</div>\n<div class=\"Con\
tSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"c\
hap2_mj.html#X867887A683961C63\">2.4 <span class=\"Heading\">Tests involving a\
utomata</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X835\
6E41086482483\">2.4-1 IsDenseAutomaton</a></span>\n<span class=\"ContSS\"><br \
/><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X8676D83880\
53F1E7\">2.4-2 IsRecognizedByAutomaton</a></span>\n<span class=\"ContSS\"><br \
/><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X80CCDD4382\
58CD25\">2.4-3 IsPermutationAutomaton</a></span>\n<span class=\"ContSS\"><br /\
><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7B7CA236808\
88C9C\">2.4-4 IsInverseAutomaton</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7A4CDEFB84B97849\
\">2.4-5 AddInverseEdgesToInverseAutomaton</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X8321BC\
E57E55FB30\">2.4-6 IsReversibleAutomaton</a></span>\n</div></div>\n<div class=\
\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a hre\
f=\"chap2_mj.html#X82EB5BE77F9F686A\">2.5 <span class=\"Heading\">Basic operat\
ions</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X8225A1\
B886131707\">2.5-1 CopyAutomaton</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X80D423A584246E2E\
\">2.5-2 NullCompletionAutomaton</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X79F052EC81135807\
\">2.5-3 ListSinkStatesAut</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X8240136E7A26B1A6\">2.5\
-4 RemovedSinkStates</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7C0526217BFE7A65\">2.5-5 Rev\
ersedAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7A4A066583C71ABE\">2.5-6 PermutedA\
utomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap2_mj.html#X7A72DDF0782E8D5E\">2.5-7 ListPermutedAut\
omata</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap2_mj.html#X7FA7DF6D87D63D67\">2.5-8 NormalizedAutomato\
n</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap2_mj.html#X7A94A77A7C65BA90\">2.5-9 UnionAutomata</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap2_mj.html#X83E772F2878546A4\">2.5-10 ProductAutomaton</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap2_mj.html#X85F6AD697DCA5765\">2.5-11 ProductOfLanguages</a></span>\n</div>\
</div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">\
&nbsp;</span><a href=\"chap2_mj.html#X79F21CB37B34A354\">2.6 <span class=\"Hea\
ding\">Links with Semigroups</span></a>\n</span>\n<div class=\"ContSSBlock\">\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap2_mj.html#X7B9994827CF94CC7\">2.6-1 TransitionSemigroup</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap2_mj.html#X7E3F29DF86A26347\">2.6-2 SyntacticSemigroupAut</a></span>\n<spa\
n class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"ch\
ap2_mj.html#X7D058F0D83D7B49B\">2.6-3 SyntacticSemigroupLang</a></span>\n</div\
></div>\n</div>\n<div class=\"ContChap\"><a href=\"chap3_mj.html#X833D31548317\
2905\">3 <span class=\"Heading\">Rational languages</span></a>\n<div class=\"C\
ontSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\
\"chap3_mj.html#X7C144D368043DE01\">3.1 <span class=\"Heading\">Rational Expre\
ssions</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X801\
EC6F38568426D\">3.1-1 RationalExpression</a></span>\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7EE5A70F\
7F237C41\">3.1-2 RatExpOnnLetters</a></span>\n<span class=\"ContSS\"><br /><sp\
an class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7DA59CBE8571796\
C\">3.1-3 RandomRatExp</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7E3AA84784019E6C\">3.1-4 S\
izeRatExp</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chap3_mj.html#X7DDB46817D6E79BE\">3.1-5 IsRationalExpr\
ession</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap3_mj.html#X8773359880149A98\">3.1-6 AlphabetOfRatExp<\
/a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</s\
pan><a href=\"chap3_mj.html#X84B9922B7C006158\">3.1-7 AlphabetOfRatExpAsList</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap3_mj.html#X786A096681CAC3CD\">3.1-8 CopyRatExp</a></span>\n</\
div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocs\
s\">&nbsp;</span><a href=\"chap3_mj.html#X7FB9270D7E8FABF3\">3.2 <span class=\
\"Heading\">Comparison of rational expressions</span></a>\n</span>\n</div>\n<d\
iv class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</sp\
an><a href=\"chap3_mj.html#X83A280D47DB3A033\">3.3 <span class=\"Heading\">Ope\
rations with rational languages</span></a>\n</span>\n<div class=\"ContSSBlock\
\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap3_mj.html#X8206BD4E82A81D8F\">3.3-1 UnionRatExp</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3\
_mj.html#X7E29107587611CE2\">3.3-2 ProductRatExp</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X\
83D8DAE6862C8A96\">3.3-3  StarRatExp</a></span>\n</div></div>\n</div>\n<div cl\
ass=\"ContChap\"><a href=\"chap4_mj.html#X814B7AD47E8EDAFA\">4 <span class=\"H\
eading\">Automata <em>versus</em> rational expressions</span></a>\n<div class=\
\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a hre\
f=\"chap4_mj.html#X7E631B92873300C1\">4.1 <span class=\"Heading\">From automat\
a to rational expressions</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap4_mj.html#X8751E3927CA4DEA1\">4.1-1 AutomatonToRatExp </a></span>\n</div><\
/div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&\
nbsp;</span><a href=\"chap4_mj.html#X8138227D7E65FC8C\">4.2 <span class=\"Head\
ing\">From rational expression to automata</span></a>\n</span>\n<div class=\"C\
ontSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;\
</span><a href=\"chap4_mj.html#X840EEB7B7DD8B03D\">4.2-1 RatExpToNDAut</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap4_mj.html#X866BCCB2788E8561\">4.2-2 RatExpToAutomaton</a></span>\n<\
/div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"noc\
ss\">&nbsp;</span><a href=\"chap4_mj.html#X85DCEFB88712056E\">4.3 <span class=\
\"Heading\">\n      Some tests on automata\n    </span></a>\n</span>\n<div cla\
ss=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap4_mj.html#X84E0143A860889A6\">4.3-1 IsEmptyLang</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap4_mj.html#X86AA1A5F7E1EEAFE\">4.3-2 IsFullLang</a></span>\n<spa\
n class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"ch\
ap4_mj.html#X8346D1B17DBF96E7\">4.3-3 AreEqualLang</a></span>\n<span class=\"C\
ontSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html\
#X7FCB176285FA5BBB\">4.3-4 IsContainedLang</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X83F1DE\
067C2D31A5\">4.3-5 AreDisjointLang</a></span>\n</div></div>\n</div>\n<div clas\
s=\"ContChap\"><a href=\"chap5_mj.html#X7919AA9384EBC6A5\">5 <span class=\"Hea\
ding\">Some functions involving automata</span></a>\n<div class=\"ContSect\"><\
span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.h\
tml#X8050E142796E0CBF\">5.1 <span class=\"Heading\">From one type to another</\
span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br />\
<span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X81E06D518428\
CA3C\">5.1-1 EpsilonToNFA</a></span>\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X81DC84E17A170270\">5.1-\
2 EpsilonToNFASet</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X871F807D79CE148C\">5.1-3 Epsilo\
nCompactedAut</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap5_mj.html#X83B0473278DC14F3\">5.1-4 ReducedNFA\
</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</\
span><a href=\"chap5_mj.html#X87D0F9F17F2BEB57\">5.1-5 NFAtoDFA</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap5_mj.html#X7B61945581FE4AC6\">5.1-6 FuseSymbolsAut</a></span>\n</div></div\
>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp\
;</span><a href=\"chap5_mj.html#X862A34E9801BEB25\">5.2 <span class=\"Heading\
\">Minimalization of an automaton</span></a>\n</span>\n<div class=\"ContSSBloc\
k\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a\
 href=\"chap5_mj.html#X7B5B5B10868FB525\">5.2-1 UsefulAutomaton</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap5_mj.html#X83C26846866AEE46\">5.2-2 MinimalizedAut</a></span>\n<span class\
=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.\
html#X7F7AE088808A5D00\">5.2-3  MinimalAutomaton</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X\
7F484D5A781BB643\">5.2-4 AccessibleStates</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X804A6BC\
979DA6E61\">5.2-5 AccessibleAutomaton</a></span>\n<span class=\"ContSS\"><br /\
><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7BAACCAF7E2\
D213B\">5.2-6 IntersectionLanguage</a></span>\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X8460C44386EE62\
25\">5.2-7 AutomatonAllPairsPaths</a></span>\n</div></div>\n</div>\n<div class\
=\"ContChap\"><a href=\"chap6_mj.html#X7AF3E5D081126EBD\">6 <span class=\"Head\
ing\">Finite regular languages</span></a>\n<div class=\"ContSect\"><span class\
=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap6_mj.html#X85643\
AEB7E7FB39A\">6.1 <span class=\"Heading\">Dealing with finite regular language\
s</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X82971FC28\
51B7B30\">6.1-1 IsFiniteRegularLanguage</a></span>\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7E48CD3E7\
8277FF7\">6.1-2 FiniteRegularLanguageToListOfWords</a></span>\n<span class=\"C\
ontSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html\
#X7F9C5C6F815773E6\">6.1-3 ListOfWordsToAutomaton</a></span>\n</div></div>\n</\
div>\n<div class=\"ContChap\"><a href=\"chapA_mj.html#X82FB3D357E1BE288\">A <s\
pan class=\"Heading\">Directed graphs</span></a>\n<div class=\"ContSect\"><spa\
n class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html\
#X82FB3D357E1BE288\">A.1 <span class=\"Heading\">Directed graphs</span></a>\n<\
/span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.html#X86CF9F66788B2A24\">A.1-1\
 RandomDiGraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chapA_mj.html#X868EE741872B932D\">A.1-2 VertexInD\
egree</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chapA_mj.html#X84DF2E8E7A7B32C6\">A.1-3 VertexOutDegree</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chapA_mj.html#X7FA6FAAE7AA8715D\">A.1-4 AutoVertexDegree</a></span\
>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hr\
ef=\"chapA_mj.html#X7BA5F1DF7DA89DC5\">A.1-5 ReversedGraph</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA\
_mj.html#X7F23780E7A12A79E\">A.1-6 AutoConnectedComponents</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA\
_mj.html#X7D5288C982F92481\">A.1-7 GraphStronglyConnectedComponents</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chapA_mj.html#X859B7C517AFBD198\">A.1-8 UnderlyingMultiGraphOfAutomaton</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chapA_mj.html#X78CF8E507E100C62\">A.1-9 UnderlyingGraphOfAutomaton\
</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</\
span><a href=\"chapA_mj.html#X78869D478792B3AD\">A.1-10 DiGraphToRelation</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chapA_mj.html#X7D63604A8413AAAF\">A.1-11 MSccAutomaton</a></span>\n<\
span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chapA_mj.html#X7971EE367B6B7F36\">A.1-12 AutoIsAcyclicGraph</a></span>\n</di\
v></div>\n</div>\n<div class=\"ContChap\"><a href=\"chapB_mj.html#X82D249F0793\
E6561\">B <span class=\"Heading\">\n      Drawing automata\n    </span></a>\n<\
div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</s\
pan><a href=\"chapB_mj.html#X7988DBAB78EA0C06\">B.1 <span class=\"Heading\">\n\
        Installing some external programs\n      </span></a>\n</span>\n</div>\
\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;\
</span><a href=\"chapB_mj.html#X84C97CA079719B11\">B.2 <span class=\"Heading\"\
>\n        Functions to draw automata\n      </span></a>\n</span>\n<div class=\
\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chapB_mj.html#X7BC2FDA77FD0237B\">B.2-1 DrawAutomaton</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chapB_mj.html#X7AEE146D8391CA3D\">B.2-2 DrawAutomata</a></span>\n<sp\
an class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"c\
hapB_mj.html#X7D17B77F829F9CCB\">B.2-3 DrawGraph</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapB_mj.html#X\
7E478FDD807853CA\">B.2-4 DrawSCCAutomaton</a></span>\n</div></div>\n<div class\
=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a hr\
ef=\"chapB_mj.html#X7F5419527FFCD1DF\">B.3 <span class=\"Heading\">Drawings ou\
tput formats</span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span class=\
\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapB_mj.html#X795DD9\
8D86A1A441\">B.4 <span class=\"Heading\">Drawings extra graph attributes</span\
></a>\n</span>\n</div>\n</div>\n<div class=\"ContChap\"><a href=\"chapC_mj.htm\
l#X7DBBB0537ADC9899\">C <span class=\"Heading\">Inverse automata and subgroups\
 of the free group</span></a>\n<div class=\"ContSect\"><span class=\"tocline\"\
><span class=\"nocss\">&nbsp;</span><a href=\"chapC_mj.html#X7DDDA5127A3D170C\
\">C.1 <span class=\"Heading\">From subgroups to inverse automata</span></a>\n\
</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapC_mj.html#X85358D097C314EB5\">C.1-\
1 GeneratorsToListRepresentation</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapC_mj.html#X80F3E10784590374\
\">C.1-2 ListToGeneratorsRepresentation</a></span>\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapC_mj.html#X7EAFF7E87\
9D115C5\">C.1-3 FlowerAutomaton</a></span>\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapC_mj.html#X7F729A4E8784D92E\
\">C.1-4 FoldFlowerAutomaton</a></span>\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapC_mj.html#X826D581D794F1BFB\">C\
.1-5 SubgroupGenToInvAut</a></span>\n</div></div>\n<div class=\"ContSect\"><sp\
an class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapC_mj.htm\
l#X85F2060A86DBE62B\">C.2 <span class=\"Heading\">From inverse automata to sub\
groups</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapC_mj.html#X81D\
A149779A167BD\">C.2-1 GeodesicTreeOfInverseAutomaton</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapC_mj.h\
tml#X7F117C43814F2CDE\">C.2-2 InverseAutomatonToGenerators</a></span>\n</div><\
/div>\n</div>\n<div class=\"ContChap\"><a href=\"chapBib_mj.html\"><span class\
=\"Heading\">References</span></a></div>\n<div class=\"ContChap\"><a href=\"ch\
apInd_mj.html\"><span class=\"Heading\">Index</span></a></div>\n<div class=\"C\
ontChap\"><a href=\"chap1_mj.html#X7DFB63A97E67C0A1\">1 <span class=\"Heading\
\">\n      Introduction\n    </span></a>\n</div>\n<div class=\"ContChap\"><a h\
ref=\"chap2_mj.html#X811E5FC2849C5644\">2 <span class=\"Heading\">Finite Autom\
ata</span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"\
nocss\">&nbsp;</span><a href=\"chap2_mj.html#X821C3B3687B1F2FF\">2.1 <span cla\
ss=\"Heading\">Automata generation</span></a>\n</span>\n<div class=\"ContSSBlo\
ck\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><\
a href=\"chap2_mj.html#X87D8222D7B50731E\">2.1-1 Automaton</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2\
_mj.html#X83CCDEF9814F1E6D\">2.1-2 IsAutomaton</a></span>\n<span class=\"ContS\
S\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7D\
39CECC7E12DD8A\">2.1-3 IsDeterministicAutomaton</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X8\
3C1148481BAA3DD\">2.1-4 IsNonDeterministicAutomaton</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.htm\
l#X81EC5331790D6022\">2.1-5 IsEpsilonAutomaton</a></span>\n<span class=\"ContS\
S\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X81\
FB5BE27903EC32\">2.1-6 String</a></span>\n<span class=\"ContSS\"><br /><span c\
lass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X801019097C93BCCC\">\
2.1-7 RandomAutomaton</a></span>\n</div></div>\n<div class=\"ContSect\"><span \
class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap2_mj.html#X\
80AB906D86BBC153\">2.2 <span class=\"Heading\">Automata internals</span></a>\n\
</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7A34B47778B50FFE\">2.2-\
1 AlphabetOfAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X8044B24B82C59BBF\">2.2-2 Al\
phabetOfAutomatonAsList</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X872BB42A81E4D0E7\">2.2-3\
 TransitionMatrixOfAutomaton</a></span>\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7B5C3CFA83FF80EA\">2\
.2-4 InitialStatesOfAutomaton</a></span>\n<span class=\"ContSS\"><br /><span c\
lass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X8408FE8487028B7F\">\
2.2-5 SetInitialStatesOfAutomaton</a></span>\n<span class=\"ContSS\"><br /><sp\
an class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X78CDDCC27D085F0\
0\">2.2-6 FinalStatesOfAutomaton</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X80689F1480F9D959\
\">2.2-7 SetFinalStatesOfAutomaton</a></span>\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7D22AD207A3D5F\
F4\">2.2-8 NumberStatesOfAutomaton</a></span>\n</div></div>\n<div class=\"Cont\
Sect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"ch\
ap2_mj.html#X8454E24E7D9FC1C2\">2.3 <span class=\"Heading\">Comparison of auto\
mata</span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span class=\"toclin\
e\"><span class=\"nocss\">&nbsp;</span><a href=\"chap2_mj.html#X867887A683961C\
63\">2.4 <span class=\"Heading\">Tests involving automata</span></a>\n</span>\
\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X8356E41086482483\">2.4-1 IsDen\
seAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap2_mj.html#X8676D8388053F1E7\">2.4-2 IsRecognized\
ByAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap2_mj.html#X80CCDD438258CD25\">2.4-3 IsPermutatio\
nAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap2_mj.html#X7B7CA23680888C9C\">2.4-4 IsInverseAuto\
maton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap2_mj.html#X7A4CDEFB84B97849\">2.4-5 AddInverseEdgesToI\
nverseAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X8321BCE57E55FB30\">2.4-6 IsRevers\
ibleAutomaton</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"\
tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap2_mj.html#X82EB5BE7\
7F9F686A\">2.5 <span class=\"Heading\">Basic operations</span></a>\n</span>\n<\
div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X8225A1B886131707\">2.5-1 CopyAuto\
maton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap2_mj.html#X80D423A584246E2E\">2.5-2 NullCompletionAuto\
maton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap2_mj.html#X79F052EC81135807\">2.5-3 ListSinkStatesAut<\
/a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</s\
pan><a href=\"chap2_mj.html#X8240136E7A26B1A6\">2.5-4 RemovedSinkStates</a></s\
pan>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a\
 href=\"chap2_mj.html#X7C0526217BFE7A65\">2.5-5 ReversedAutomaton</a></span>\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap2_mj.html#X7A4A066583C71ABE\">2.5-6 PermutedAutomaton</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
2_mj.html#X7A72DDF0782E8D5E\">2.5-7 ListPermutedAutomata</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_m\
j.html#X7FA7DF6D87D63D67\">2.5-8 NormalizedAutomaton</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.h\
tml#X7A94A77A7C65BA90\">2.5-9 UnionAutomata</a></span>\n<span class=\"ContSS\"\
><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X83E77\
2F2878546A4\">2.5-10 ProductAutomaton</a></span>\n<span class=\"ContSS\"><br /\
><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X85F6AD697DC\
A5765\">2.5-11 ProductOfLanguages</a></span>\n</div></div>\n<div class=\"ContS\
ect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"cha\
p2_mj.html#X79F21CB37B34A354\">2.6 <span class=\"Heading\">Links with Semigrou\
ps</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7B999482\
7CF94CC7\">2.6-1 TransitionSemigroup</a></span>\n<span class=\"ContSS\"><br />\
<span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7E3F29DF86A2\
6347\">2.6-2 SyntacticSemigroupAut</a></span>\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7D058F0D83D7B4\
9B\">2.6-3 SyntacticSemigroupLang</a></span>\n</div></div>\n</div>\n<div class\
=\"ContChap\"><a href=\"chap3_mj.html#X833D315483172905\">3 <span class=\"Head\
ing\">Rational languages</span></a>\n<div class=\"ContSect\"><span class=\"toc\
line\"><span class=\"nocss\">&nbsp;</span><a href=\"chap3_mj.html#X7C144D36804\
3DE01\">3.1 <span class=\"Heading\">Rational Expressions</span></a>\n</span>\n\
<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X801EC6F38568426D\">3.1-1 Ration\
alExpression</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap3_mj.html#X7EE5A70F7F237C41\">3.1-2 RatExpOnnLe\
tters</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X7DA59CBE8571796C\">3.1-3 RandomRatExp</a></\
span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><\
a href=\"chap3_mj.html#X7E3AA84784019E6C\">3.1-4 SizeRatExp</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
3_mj.html#X7DDB46817D6E79BE\">3.1-5 IsRationalExpression</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_m\
j.html#X8773359880149A98\">3.1-6 AlphabetOfRatExp</a></span>\n<span class=\"Co\
ntSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#\
X84B9922B7C006158\">3.1-7 AlphabetOfRatExpAsList</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X\
786A096681CAC3CD\">3.1-8 CopyRatExp</a></span>\n</div></div>\n<div class=\"Con\
tSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"c\
hap3_mj.html#X7FB9270D7E8FABF3\">3.2 <span class=\"Heading\">Comparison of rat\
ional expressions</span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span c\
lass=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap3_mj.html#X8\
3A280D47DB3A033\">3.3 <span class=\"Heading\">Operations with rational languag\
es</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8206BD4E\
82A81D8F\">3.3-1 UnionRatExp</a></span>\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7E29107587611CE2\">3\
.3-2 ProductRatExp</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X83D8DAE6862C8A96\">3.3-3  Star\
RatExp</a></span>\n</div></div>\n</div>\n<div class=\"ContChap\"><a href=\"cha\
p4_mj.html#X814B7AD47E8EDAFA\">4 <span class=\"Heading\">Automata <em>versus</\
em> rational expressions</span></a>\n<div class=\"ContSect\"><span class=\"toc\
line\"><span class=\"nocss\">&nbsp;</span><a href=\"chap4_mj.html#X7E631B92873\
300C1\">4.1 <span class=\"Heading\">From automata to rational expressions</spa\
n></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><sp\
an class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X8751E3927CA4DEA\
1\">4.1-1 AutomatonToRatExp </a></span>\n</div></div>\n<div class=\"ContSect\"\
><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap4_mj\
.html#X8138227D7E65FC8C\">4.2 <span class=\"Heading\">From rational expression\
 to automata</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"C\
ontSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html\
#X840EEB7B7DD8B03D\">4.2-1 RatExpToNDAut</a></span>\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X866BCCB2\
788E8561\">4.2-2 RatExpToAutomaton</a></span>\n</div></div>\n<div class=\"Cont\
Sect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"ch\
ap4_mj.html#X85DCEFB88712056E\">4.3 <span class=\"Heading\">\n      Some tests\
 on automata\n    </span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap4_m\
j.html#X84E0143A860889A6\">4.3-1 IsEmptyLang</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X86A\
A1A5F7E1EEAFE\">4.3-2 IsFullLang</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X8346D1B17DBF96E7\
\">4.3-3 AreEqualLang</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X7FCB176285FA5BBB\">4.3-4 Is\
ContainedLang</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap4_mj.html#X83F1DE067C2D31A5\">4.3-5 AreDisjoin\
tLang</a></span>\n</div></div>\n</div>\n<div class=\"ContChap\"><a href=\"chap\
5_mj.html#X7919AA9384EBC6A5\">5 <span class=\"Heading\">Some functions involvi\
ng automata</span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span \
class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X8050E142796E0CBF\">5.1 <\
span class=\"Heading\">From one type to another</span></a>\n</span>\n<div clas\
s=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap5_mj.html#X81E06D518428CA3C\">5.1-1 EpsilonToNFA</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap5_mj.html#X81DC84E17A170270\">5.1-2 EpsilonToNFASet</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap5_mj.html#X871F807D79CE148C\">5.1-3 EpsilonCompactedAut</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap5_mj.html#X83B0473278DC14F3\">5.1-4 ReducedNFA</a></span>\n<span class=\"C\
ontSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html\
#X87D0F9F17F2BEB57\">5.1-5 NFAtoDFA</a></span>\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7B61945581FE4\
AC6\">5.1-6 FuseSymbolsAut</a></span>\n</div></div>\n<div class=\"ContSect\"><\
span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.h\
tml#X862A34E9801BEB25\">5.2 <span class=\"Heading\">Minimalization of an autom\
aton</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7B5B5B\
10868FB525\">5.2-1 UsefulAutomaton</a></span>\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X83C26846866AEE\
46\">5.2-2 MinimalizedAut</a></span>\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7F7AE088808A5D00\">5.2-\
3  MinimalAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7F484D5A781BB643\">5.2-4 Acce\
ssibleStates</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap5_mj.html#X804A6BC979DA6E61\">5.2-5 AccessibleA\
utomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap5_mj.html#X7BAACCAF7E2D213B\">5.2-6 IntersectionLan\
guage</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap5_mj.html#X8460C44386EE6225\">5.2-7 AutomatonAllPairsP\
aths</a></span>\n</div></div>\n</div>\n<div class=\"ContChap\"><a href=\"chap6\
_mj.html#X7AF3E5D081126EBD\">6 <span class=\"Heading\">Finite regular language\
s</span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"no\
css\">&nbsp;</span><a href=\"chap6_mj.html#X85643AEB7E7FB39A\">6.1 <span class\
=\"Heading\">Dealing with finite regular languages</span></a>\n</span>\n<div c\
lass=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap6_mj.html#X82971FC2851B7B30\">6.1-1 IsFiniteRegul\
arLanguage</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap6_mj.html#X7E48CD3E78277FF7\">6.1-2 FiniteRegular\
LanguageToListOfWords</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7F9C5C6F815773E6\">6.1-3 Li\
stOfWordsToAutomaton</a></span>\n</div></div>\n</div>\n<div class=\"ContChap\"\
><a href=\"chapA_mj.html#X82FB3D357E1BE288\">A <span class=\"Heading\">Directe\
d graphs</span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span cla\
ss=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html#X82FB3D357E1BE288\">A.1 <spa\
n class=\"Heading\">Directed graphs</span></a>\n</span>\n<div class=\"ContSSBl\
ock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chapA_mj.html#X86CF9F66788B2A24\">A.1-1 RandomDiGraph</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chapA_mj.html#X868EE741872B932D\">A.1-2 VertexInDegree</a></span>\n<span class\
=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.\
html#X84DF2E8E7A7B32C6\">A.1-3 VertexOutDegree</a></span>\n<span class=\"ContS\
S\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.html#X7F\
A6FAAE7AA8715D\">A.1-4 AutoVertexDegree</a></span>\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.html#X7BA5F1DF7\
DA89DC5\">A.1-5 ReversedGraph</a></span>\n<span class=\"ContSS\"><br /><span c\
lass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.html#X7F23780E7A12A79E\">\
A.1-6 AutoConnectedComponents</a></span>\n<span class=\"ContSS\"><br /><span c\
lass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.html#X7D5288C982F92481\">\
A.1-7 GraphStronglyConnectedComponents</a></span>\n<span class=\"ContSS\"><br \
/><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.html#X859B7C517A\
FBD198\">A.1-8 UnderlyingMultiGraphOfAutomaton</a></span>\n<span class=\"ContS\
S\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.html#X78\
CF8E507E100C62\">A.1-9 UnderlyingGraphOfAutomaton</a></span>\n<span class=\"Co\
ntSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.html#\
X78869D478792B3AD\">A.1-10 DiGraphToRelation</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.html#X7D6\
3604A8413AAAF\">A.1-11 MSccAutomaton</a></span>\n<span class=\"ContSS\"><br />\
<span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapA_mj.html#X7971EE367B6B\
7F36\">A.1-12 AutoIsAcyclicGraph</a></span>\n</div></div>\n</div>\n<div class=\
\"ContChap\"><a href=\"chapB_mj.html#X82D249F0793E6561\">B <span class=\"Headi\
ng\">\n      Drawing automata\n    </span></a>\n<div class=\"ContSect\"><span \
class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapB_mj.html#X\
7988DBAB78EA0C06\">B.1 <span class=\"Heading\">\n        Installing some exter\
nal programs\n      </span></a>\n</span>\n</div>\n<div class=\"ContSect\"><spa\
n class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapB_mj.html\
#X84C97CA079719B11\">B.2 <span class=\"Heading\">\n        Functions to draw a\
utomata\n      </span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapB_mj.h\
tml#X7BC2FDA77FD0237B\">B.2-1 DrawAutomaton</a></span>\n<span class=\"ContSS\"\
><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapB_mj.html#X7AEE1\
46D8391CA3D\">B.2-2 DrawAutomata</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chapB_mj.html#X7D17B77F829F9CCB\
\">B.2-3 DrawGraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chapB_mj.html#X7E478FDD807853CA\">B.2-4 DrawS\
CCAutomaton</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"to\
cline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapB_mj.html#X7F5419527F\
FCD1DF\">B.3 <span class=\"Heading\">Drawings output formats</span></a>\n</spa\
n>\n</div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocs\
s\">&nbsp;</span><a href=\"chapB_mj.html#X795DD98D86A1A441\">B.4 <span class=\
\"Heading\">Drawings extra graph attributes</span></a>\n</span>\n</div>\n</div\
>\n<div class=\"ContChap\"><a href=\"chapC_mj.html#X7DBBB0537ADC9899\">C <span\
 class=\"Heading\">Inverse automata and subgroups of the free group</span></a>\
\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;\
</span><a href=\"chapC_mj.html#X7DDDA5127A3D170C\">C.1 <span class=\"Heading\"\
>From subgroups to inverse automata</span></a>\n</span>\n<div class=\"ContSSBl\
ock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chapC_mj.html#X85358D097C314EB5\">C.1-1 GeneratorsToListRepresentati\
on</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;\
</span><a href=\"chapC_mj.html#X80F3E10784590374\">C.1-2 ListToGeneratorsRepre\
sentation</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chapC_mj.html#X7EAFF7E879D115C5\">C.1-3 FlowerAutomato\
n</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chapC_mj.html#X7F729A4E8784D92E\">C.1-4 FoldFlowerAutomaton</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chapC_mj.html#X826D581D794F1BFB\">C.1-5 SubgroupGenToInvAut</a></s\
pan>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span clas\
s=\"nocss\">&nbsp;</span><a href=\"chapC_mj.html#X85F2060A86DBE62B\">C.2 <span\
 class=\"Heading\">From inverse automata to subgroups</span></a>\n</span>\n<di\
v class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chapC_mj.html#X81DA149779A167BD\">C.2-1 GeodesicTr\
eeOfInverseAutomaton</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chapC_mj.html#X7F117C43814F2CDE\">C.2-2 Inv\
erseAutomatonToGenerators</a></span>\n</div></div>\n</div>\n<div class=\"ContC\
hap\"><a href=\"chapBib_mj.html\"><span class=\"Heading\">References</span></a\
></div>\n<div class=\"ContChap\"><a href=\"chapInd_mj.html\"><span class=\"Hea\
ding\">Index</span></a></div>\n" )
gap> gap> #I  File: /builddir/build/BUILD/automata/../pkg/automata/doc/manual.lab written.
gap> + rm -fr ../../doc ../pkg
+ exit 0
Executing(%install): /bin/sh -e /var/tmp/rpm-tmp.TKmiTD
+ umask 022
+ cd /builddir/build/BUILD
+ '[' /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64 '!=' / ']'
+ rm -rf /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64
++ dirname /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64
+ mkdir -p /builddir/build/BUILDROOT
+ mkdir /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64
+ cd automata
+ mkdir -p /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg
+ cp -a ../automata /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata
+ rm -f /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/CHANGES /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/EXAMPLES /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/LICENSE /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/README
+ rm -f '/builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/doc/*.aux' /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/doc/AutMan.bbl /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/doc/AutMan.blg /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/doc/AutMan.brf /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/doc/AutMan.idx /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/doc/AutMan.ilg /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/doc/AutMan.ind '/builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/doc/*.log' /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/doc/AutMan.out /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/doc/AutMan.pnr /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/doc/AutMan.tex /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/lib/gap/pkg/automata/doc/AutMan.toc
+ /usr/lib/rpm/find-debuginfo.sh --strict-build-id -m --run-dwz --dwz-low-mem-die-limit 10000000 --dwz-max-die-limit 110000000 /builddir/build/BUILD/automata
/usr/lib/rpm/sepdebugcrcfix: Updated 0 CRC32s, 0 CRC32s did match.
find: 'debug': No such file or directory
+ /usr/lib/rpm/check-buildroot
+ /usr/lib/rpm/redhat/brp-compress
+ /usr/lib/rpm/redhat/brp-strip-static-archive /usr/bin/strip
+ /usr/lib/rpm/brp-python-bytecompile /usr/bin/python 1
+ /usr/lib/rpm/redhat/brp-python-hardlink
+ /usr/lib/rpm/redhat/brp-java-repack-jars
Processing files: gap-pkg-automata-1.13-0.3.el7.centos.noarch
Executing(%doc): /bin/sh -e /var/tmp/rpm-tmp.PACgTv
+ umask 022
+ cd /builddir/build/BUILD
+ cd automata
+ DOCDIR=/builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/share/doc/gap-pkg-automata-1.13
+ export DOCDIR
+ /usr/bin/mkdir -p /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/share/doc/gap-pkg-automata-1.13
+ cp -pr CHANGES /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/share/doc/gap-pkg-automata-1.13
+ cp -pr EXAMPLES /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/share/doc/gap-pkg-automata-1.13
+ cp -pr README /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/share/doc/gap-pkg-automata-1.13
+ exit 0
Executing(%license): /bin/sh -e /var/tmp/rpm-tmp.Ry2LUn
+ umask 022
+ cd /builddir/build/BUILD
+ cd automata
+ LICENSEDIR=/builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/share/licenses/gap-pkg-automata-1.13
+ export LICENSEDIR
+ /usr/bin/mkdir -p /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/share/licenses/gap-pkg-automata-1.13
+ cp -pr LICENSE /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64/usr/share/licenses/gap-pkg-automata-1.13
+ exit 0
Provides: gap-pkg-automata = 1.13-0.3.el7.centos
Requires(rpmlib): rpmlib(CompressedFileNames) <= 3.0.4-1 rpmlib(FileDigests) <= 4.6.0-1 rpmlib(PayloadFilesHavePrefix) <= 4.0-1
Checking for unpackaged file(s): /usr/lib/rpm/check-files /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64
Wrote: /builddir/build/RPMS/gap-pkg-automata-1.13-0.3.el7.centos.noarch.rpm
Executing(%clean): /bin/sh -e /var/tmp/rpm-tmp.HlNzTc
+ umask 022
+ cd /builddir/build/BUILD
+ cd automata
+ /usr/bin/rm -rf /builddir/build/BUILDROOT/gap-pkg-automata-1.13-0.3.el7.centos.x86_64
+ exit 0
Finish: rpmbuild gap-pkg-automata-1.13-0.3.el7.centos.src.rpm
Finish: build phase for gap-pkg-automata-1.13-0.3.el7.centos.src.rpm
INFO: Done(intermediate-srpm/gap-pkg-automata-1.13-0.3.el7.centos.src.rpm) Config(child) 1 minutes 3 seconds
INFO: Results and/or logs in: /var/lib/copr-rpmbuild/results
INFO: Cleaning up build root ('cleanup_on_success=True')
Start: clean chroot
INFO: unmounting tmpfs.
Finish: clean chroot
Finish: run