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<h1><span class="URL"><a href="https://gap-packages.github.io/automata/">Automata</a></span></h1>


<h2>A package on automata</h2>

<p> Version 1.16</p>

</div>
<p><b>
    Manuel Delgado




  </b>
<br />Email: <span class="URL"><a href="mailto:mdelgado@fc.up.pt">mdelgado@fc.up.pt</a></span>
<br />Homepage: <span class="URL"><a href="https://cmup.fc.up.pt/cmup/mdelgado/">https://cmup.fc.up.pt/cmup/mdelgado/</a></span>
<br />Address: <br />Departamento de Matemática - Faculdade de Ciências<br /> Porto<br /> Portugal<br />
</p><p><b>
    Steve Linton




  </b>
<br />Email: <span class="URL"><a href="mailto:steve.linton@st-andrews.ac.uk">steve.linton@st-andrews.ac.uk</a></span>
<br />Homepage: <span class="URL"><a href="http://www-groups.dcs.st-and.ac.uk/~sal/">http://www-groups.dcs.st-and.ac.uk/~sal/</a></span>
<br />Address: <br />School of Computer Science<br /> University of St Andrews<br /> Jack Cole Building, North Haugh<br /> St Andrews, Fife, KY16 9SX<br /> United Kingdom<br />
</p><p><b>
    José João Morais


  </b>
<br />Address: <br />No address known<br />
</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2004 by Manuel Delgado, Steve Linton and José Morais</p>

<p><span class="URL"><a href="https://gap-packages.github.io/automata/">Automata</a></span> package is free software; you can redistribute it and/or modify it under the terms of the <span class="URL"><a href="https://www.fsf.org/licenses/gpl.html">GNU General Public License</a></span> as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. For details, see the file 'GPL' included in the package or see the FSF's own site.



<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>The first author wishes to acknowledge Cyril Nicaud and Paulo Varandas for their help in programming some functions of the very first version of this package. He wishes also to acknowledge useful discussions and comments by Cyril Nicaud, Vítor H. Fernandes, Jean-Eric Pin and Jorge Almeida.</p>

<p>The first author also acknowledges support of FCT through CMUP and the FCT and POCTI Project POCTI/32817/MAT/2000 which is funded in cooperation with the European Community Fund FEDER.</p>

<p>The third author acknowledges financial support of FCT and the POCTI program through a scholarship given by Centro de Matemática da Universidade do Porto.</p>

<p>The authors would like to thank Mark Kambites for his contribution in finding bugs and making suggestions for the improvement of this package.</p>

<p>Concerning the maintenance:</p>

<p>The first author was/is (partially) supported by:</p>

<p>the Fundação para a Ciência e a Tecnologia (FCT) project PTDC/MAT/65481/2006;</p>

<p>the <em>Centro de Matemática da Universidade do Porto</em> (CMUP), in particular for those periods in which CMUP was funded by</p>

<p>the European Regional Development Fund through the program COMPETE and by the Portuguese Government through the FCT - Fundação para a Ciência e a Tecnologia under the project PEst-C/MAT/UI0144/2011;</p>

<p>The first author wants to acknowledge partial support by CMUP (UID/MAT/00144/2013 and UID/MAT/00144/2019), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020.</p>

<p><a id="X7982162280BC7A61" name="X7982162280BC7A61"></a></p>
<h3>Colophon</h3>
<p>This work started in 1998, when the first author was in the LIAFA at the University of Paris 7, in a post-doc. Encouraged by J. E. Pin, he began the implementation in <strong class="pkg">GAP</strong>3 of an algorithm obtained some time before to answer a question from the realm of Finite Semigroups proposed by J. Almeida.</p>

<p>The first version of this package on automata was prepared by the first author who gave it the form of a <strong class="pkg">GAP</strong> share package. In a second version, prepared by the first and third authors, many functions have been added and the performance of many of the existing ones has been improved. Further important improvements, specially concerning performance, have been achieved when the second author joined the group. The first author is particularly grateful to Max Horn whose help made the release of Versions 1.14 and 1.15 a lot easier.</p>

<p>From Version 1.12, the package is maintained by the first two authors, and Ruth Hoffmann joined the maintenance team from Version 1.16. Bug reports, suggestions and comments are welcome. Please use our email addresses to this effect.</p>

<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>

<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">
      Introduction
    </span></a>
</div>
<div class="ContChap"><a href="chap2.html#X811E5FC2849C5644">2 <span class="Heading">Finite Automata</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X821C3B3687B1F2FF">2.1 <span class="Heading">Automata generation</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X87D8222D7B50731E">2.1-1 Automaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X83CCDEF9814F1E6D">2.1-2 IsAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7D39CECC7E12DD8A">2.1-3 IsDeterministicAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X83C1148481BAA3DD">2.1-4 IsNonDeterministicAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X81EC5331790D6022">2.1-5 IsEpsilonAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X81FB5BE27903EC32">2.1-6 String</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X801019097C93BCCC">2.1-7 RandomAutomaton</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X80AB906D86BBC153">2.2 <span class="Heading">Automata internals</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7A34B47778B50FFE">2.2-1 AlphabetOfAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8044B24B82C59BBF">2.2-2 AlphabetOfAutomatonAsList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X872BB42A81E4D0E7">2.2-3 TransitionMatrixOfAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7B5C3CFA83FF80EA">2.2-4 InitialStatesOfAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8408FE8487028B7F">2.2-5 SetInitialStatesOfAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X78CDDCC27D085F00">2.2-6 FinalStatesOfAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X80689F1480F9D959">2.2-7 SetFinalStatesOfAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7D22AD207A3D5FF4">2.2-8 NumberStatesOfAutomaton</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X8454E24E7D9FC1C2">2.3 <span class="Heading">Comparison of automata</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X867887A683961C63">2.4 <span class="Heading">Tests involving automata</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8356E41086482483">2.4-1 IsDenseAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8676D8388053F1E7">2.4-2 IsRecognizedByAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X80CCDD438258CD25">2.4-3 IsPermutationAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7B7CA23680888C9C">2.4-4 IsInverseAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7A4CDEFB84B97849">2.4-5 AddInverseEdgesToInverseAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8321BCE57E55FB30">2.4-6 IsReversibleAutomaton</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X82EB5BE77F9F686A">2.5 <span class="Heading">Basic operations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8225A1B886131707">2.5-1 CopyAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X80D423A584246E2E">2.5-2 NullCompletionAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X79F052EC81135807">2.5-3 ListSinkStatesAut</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8240136E7A26B1A6">2.5-4 RemovedSinkStates</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7C0526217BFE7A65">2.5-5 ReversedAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7A4A066583C71ABE">2.5-6 PermutedAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7A72DDF0782E8D5E">2.5-7 ListPermutedAutomata</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7FA7DF6D87D63D67">2.5-8 NormalizedAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7A94A77A7C65BA90">2.5-9 UnionAutomata</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X83E772F2878546A4">2.5-10 ProductAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X85F6AD697DCA5765">2.5-11 ProductOfLanguages</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X79F21CB37B34A354">2.6 <span class="Heading">Links with Semigroups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7B9994827CF94CC7">2.6-1 TransitionSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7E3F29DF86A26347">2.6-2 SyntacticSemigroupAut</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7D058F0D83D7B49B">2.6-3 SyntacticSemigroupLang</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap3.html#X833D315483172905">3 <span class="Heading">Rational languages</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7C144D368043DE01">3.1 <span class="Heading">Rational Expressions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X801EC6F38568426D">3.1-1 RationalExpression</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7EE5A70F7F237C41">3.1-2 RatExpOnnLetters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7DA59CBE8571796C">3.1-3 RandomRatExp</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7E3AA84784019E6C">3.1-4 SizeRatExp</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7DDB46817D6E79BE">3.1-5 IsRationalExpression</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8773359880149A98">3.1-6 AlphabetOfRatExp</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X84B9922B7C006158">3.1-7 AlphabetOfRatExpAsList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X786A096681CAC3CD">3.1-8 CopyRatExp</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7FB9270D7E8FABF3">3.2 <span class="Heading">Comparison of rational expressions</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X83A280D47DB3A033">3.3 <span class="Heading">Operations with rational languages</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8206BD4E82A81D8F">3.3-1 UnionRatExp</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7E29107587611CE2">3.3-2 ProductRatExp</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X83D8DAE6862C8A96">3.3-3  StarRatExp</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4.html#X7B5CD9B7796BD926">4 <span class="Heading">Automata <em>versus</em> rational expressions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7E631B92873300C1">4.1 <span class="Heading">From automata to rational expressions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8751E3927CA4DEA1">4.1-1 AutomatonToRatExp </a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X8138227D7E65FC8C">4.2 <span class="Heading">From rational expression to automata</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X840EEB7B7DD8B03D">4.2-1 RatExpToNDAut</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X866BCCB2788E8561">4.2-2 RatExpToAutomaton</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X85DCEFB88712056E">4.3 <span class="Heading">
      Some tests on automata
    </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X84E0143A860889A6">4.3-1 IsEmptyLang</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X86AA1A5F7E1EEAFE">4.3-2 IsFullLang</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8346D1B17DBF96E7">4.3-3 AreEqualLang</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7FCB176285FA5BBB">4.3-4 IsContainedLang</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X83F1DE067C2D31A5">4.3-5 AreDisjointLang</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap5.html#X7919AA9384EBC6A5">5 <span class="Heading">Some functions involving automata</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X8050E142796E0CBF">5.1 <span class="Heading">From one type to another</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X81E06D518428CA3C">5.1-1 EpsilonToNFA</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X81DC84E17A170270">5.1-2 EpsilonToNFASet</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X871F807D79CE148C">5.1-3 EpsilonCompactedAut</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X83B0473278DC14F3">5.1-4 ReducedNFA</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X87D0F9F17F2BEB57">5.1-5 NFAtoDFA</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7B61945581FE4AC6">5.1-6 FuseSymbolsAut</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X862A34E9801BEB25">5.2 <span class="Heading">Minimalization of an automaton</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7B5B5B10868FB525">5.2-1 UsefulAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X83C26846866AEE46">5.2-2 MinimalizedAut</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7F7AE088808A5D00">5.2-3  MinimalAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7F484D5A781BB643">5.2-4 AccessibleStates</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X804A6BC979DA6E61">5.2-5 AccessibleAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7BAACCAF7E2D213B">5.2-6 IntersectionLanguage</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X8460C44386EE6225">5.2-7 AutomatonAllPairsPaths</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap6.html#X7AF3E5D081126EBD">6 <span class="Heading">Finite regular languages</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X85643AEB7E7FB39A">6.1 <span class="Heading">Dealing with finite regular languages</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X82971FC2851B7B30">6.1-1 IsFiniteRegularLanguage</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7E48CD3E78277FF7">6.1-2 FiniteRegularLanguageToListOfWords</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7F9C5C6F815773E6">6.1-3 ListOfWordsToAutomaton</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapA.html#X82FB3D357E1BE288">A <span class="Heading">Directed graphs</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA.html#X82FB3D357E1BE288">A.1 <span class="Heading">Directed graphs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapA.html#X86CF9F66788B2A24">A.1-1 RandomDiGraph</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapA.html#X868EE741872B932D">A.1-2 VertexInDegree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapA.html#X84DF2E8E7A7B32C6">A.1-3 VertexOutDegree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapA.html#X7FA6FAAE7AA8715D">A.1-4 AutoVertexDegree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapA.html#X7BA5F1DF7DA89DC5">A.1-5 ReversedGraph</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapA.html#X7F23780E7A12A79E">A.1-6 AutoConnectedComponents</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapA.html#X7D5288C982F92481">A.1-7 GraphStronglyConnectedComponents</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapA.html#X859B7C517AFBD198">A.1-8 UnderlyingMultiGraphOfAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapA.html#X78CF8E507E100C62">A.1-9 UnderlyingGraphOfAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapA.html#X78869D478792B3AD">A.1-10 DiGraphToRelation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapA.html#X7D63604A8413AAAF">A.1-11 MSccAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapA.html#X7971EE367B6B7F36">A.1-12 AutoIsAcyclicGraph</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapB.html#X82D249F0793E6561">B <span class="Heading">
      Drawing automata
    </span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapB.html#X7988DBAB78EA0C06">B.1 <span class="Heading">
        Installing some external programs
      </span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapB.html#X84C97CA079719B11">B.2 <span class="Heading">
        Functions to draw automata
      </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapB.html#X7BC2FDA77FD0237B">B.2-1 DrawAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapB.html#X7896CAD4832C7748">B.2-2 DotForDrawingAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapB.html#X84DF99868747DD69">B.2-3 DrawSubAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapB.html#X7BB5015378320678">B.2-4 DotStringForDrawingSubAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapB.html#X7870774E83892026">B.2-5 DotStringForDrawingGraph</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapB.html#X7E478FDD807853CA">B.2-6 DrawSCCAutomaton</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapC.html#X7DBBB0537ADC9899">C <span class="Heading">Inverse automata and subgroups of the free group</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapC.html#X7DDDA5127A3D170C">C.1 <span class="Heading">From subgroups to inverse automata</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapC.html#X85358D097C314EB5">C.1-1 GeneratorsToListRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapC.html#X80F3E10784590374">C.1-2 ListToGeneratorsRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapC.html#X7EAFF7E879D115C5">C.1-3 FlowerAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapC.html#X7F729A4E8784D92E">C.1-4 FoldFlowerAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapC.html#X826D581D794F1BFB">C.1-5 SubgroupGenToInvAut</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapC.html#X85F2060A86DBE62B">C.2 <span class="Heading">From inverse automata to subgroups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapC.html#X81DA149779A167BD">C.2-1 GeodesicTreeOfInverseAutomaton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapC.html#X7F117C43814F2CDE">C.2-2 InverseAutomatonToGenerators</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
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