\contentsline {chapter}{\numberline {1}\leavevmode {\color {Chapter } Introduction }}{6}{chapter.1}
\contentsline {chapter}{\numberline {2}\leavevmode {\color {Chapter }Finite Automata}}{8}{chapter.2}
\contentsline {section}{\numberline {2.1}\leavevmode {\color {Chapter }Automata generation}}{8}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}\leavevmode {\color {Chapter }Automaton}}{8}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}\leavevmode {\color {Chapter }IsAutomaton}}{10}{subsection.2.1.2}
\contentsline {subsection}{\numberline {2.1.3}\leavevmode {\color {Chapter }IsDeterministicAutomaton}}{10}{subsection.2.1.3}
\contentsline {subsection}{\numberline {2.1.4}\leavevmode {\color {Chapter }IsNonDeterministicAutomaton}}{10}{subsection.2.1.4}
\contentsline {subsection}{\numberline {2.1.5}\leavevmode {\color {Chapter }IsEpsilonAutomaton}}{10}{subsection.2.1.5}
\contentsline {subsection}{\numberline {2.1.6}\leavevmode {\color {Chapter }String}}{11}{subsection.2.1.6}
\contentsline {subsection}{\numberline {2.1.7}\leavevmode {\color {Chapter }RandomAutomaton}}{11}{subsection.2.1.7}
\contentsline {section}{\numberline {2.2}\leavevmode {\color {Chapter }Automata internals}}{12}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}\leavevmode {\color {Chapter }AlphabetOfAutomaton}}{12}{subsection.2.2.1}
\contentsline {subsection}{\numberline {2.2.2}\leavevmode {\color {Chapter }AlphabetOfAutomatonAsList}}{12}{subsection.2.2.2}
\contentsline {subsection}{\numberline {2.2.3}\leavevmode {\color {Chapter }TransitionMatrixOfAutomaton}}{13}{subsection.2.2.3}
\contentsline {subsection}{\numberline {2.2.4}\leavevmode {\color {Chapter }InitialStatesOfAutomaton}}{13}{subsection.2.2.4}
\contentsline {subsection}{\numberline {2.2.5}\leavevmode {\color {Chapter }SetInitialStatesOfAutomaton}}{13}{subsection.2.2.5}
\contentsline {subsection}{\numberline {2.2.6}\leavevmode {\color {Chapter }FinalStatesOfAutomaton}}{13}{subsection.2.2.6}
\contentsline {subsection}{\numberline {2.2.7}\leavevmode {\color {Chapter }SetFinalStatesOfAutomaton}}{14}{subsection.2.2.7}
\contentsline {subsection}{\numberline {2.2.8}\leavevmode {\color {Chapter }NumberStatesOfAutomaton}}{14}{subsection.2.2.8}
\contentsline {section}{\numberline {2.3}\leavevmode {\color {Chapter }Comparison of automata}}{14}{section.2.3}
\contentsline {section}{\numberline {2.4}\leavevmode {\color {Chapter }Tests involving automata}}{14}{section.2.4}
\contentsline {subsection}{\numberline {2.4.1}\leavevmode {\color {Chapter }IsDenseAutomaton}}{14}{subsection.2.4.1}
\contentsline {subsection}{\numberline {2.4.2}\leavevmode {\color {Chapter }IsRecognizedByAutomaton}}{15}{subsection.2.4.2}
\contentsline {subsection}{\numberline {2.4.3}\leavevmode {\color {Chapter }IsPermutationAutomaton}}{15}{subsection.2.4.3}
\contentsline {subsection}{\numberline {2.4.4}\leavevmode {\color {Chapter }IsInverseAutomaton}}{15}{subsection.2.4.4}
\contentsline {subsection}{\numberline {2.4.5}\leavevmode {\color {Chapter }AddInverseEdgesToInverseAutomaton}}{15}{subsection.2.4.5}
\contentsline {subsection}{\numberline {2.4.6}\leavevmode {\color {Chapter }IsReversibleAutomaton}}{16}{subsection.2.4.6}
\contentsline {section}{\numberline {2.5}\leavevmode {\color {Chapter }Basic operations}}{16}{section.2.5}
\contentsline {subsection}{\numberline {2.5.1}\leavevmode {\color {Chapter }CopyAutomaton}}{16}{subsection.2.5.1}
\contentsline {subsection}{\numberline {2.5.2}\leavevmode {\color {Chapter }NullCompletionAutomaton}}{16}{subsection.2.5.2}
\contentsline {subsection}{\numberline {2.5.3}\leavevmode {\color {Chapter }ListSinkStatesAut}}{17}{subsection.2.5.3}
\contentsline {subsection}{\numberline {2.5.4}\leavevmode {\color {Chapter }RemovedSinkStates}}{17}{subsection.2.5.4}
\contentsline {subsection}{\numberline {2.5.5}\leavevmode {\color {Chapter }ReversedAutomaton}}{17}{subsection.2.5.5}
\contentsline {subsection}{\numberline {2.5.6}\leavevmode {\color {Chapter }PermutedAutomaton}}{18}{subsection.2.5.6}
\contentsline {subsection}{\numberline {2.5.7}\leavevmode {\color {Chapter }ListPermutedAutomata}}{18}{subsection.2.5.7}
\contentsline {subsection}{\numberline {2.5.8}\leavevmode {\color {Chapter }NormalizedAutomaton}}{18}{subsection.2.5.8}
\contentsline {subsection}{\numberline {2.5.9}\leavevmode {\color {Chapter }UnionAutomata}}{19}{subsection.2.5.9}
\contentsline {subsection}{\numberline {2.5.10}\leavevmode {\color {Chapter }ProductAutomaton}}{19}{subsection.2.5.10}
\contentsline {subsection}{\numberline {2.5.11}\leavevmode {\color {Chapter }ProductOfLanguages}}{20}{subsection.2.5.11}
\contentsline {section}{\numberline {2.6}\leavevmode {\color {Chapter }Links with Semigroups}}{20}{section.2.6}
\contentsline {subsection}{\numberline {2.6.1}\leavevmode {\color {Chapter }TransitionSemigroup}}{20}{subsection.2.6.1}
\contentsline {subsection}{\numberline {2.6.2}\leavevmode {\color {Chapter }SyntacticSemigroupAut}}{21}{subsection.2.6.2}
\contentsline {subsection}{\numberline {2.6.3}\leavevmode {\color {Chapter }SyntacticSemigroupLang}}{21}{subsection.2.6.3}
\contentsline {chapter}{\numberline {3}\leavevmode {\color {Chapter }Rational languages}}{22}{chapter.3}
\contentsline {section}{\numberline {3.1}\leavevmode {\color {Chapter }Rational Expressions}}{22}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}\leavevmode {\color {Chapter }RationalExpression}}{22}{subsection.3.1.1}
\contentsline {subsection}{\numberline {3.1.2}\leavevmode {\color {Chapter }RatExpOnnLetters}}{22}{subsection.3.1.2}
\contentsline {subsection}{\numberline {3.1.3}\leavevmode {\color {Chapter }RandomRatExp}}{23}{subsection.3.1.3}
\contentsline {subsection}{\numberline {3.1.4}\leavevmode {\color {Chapter }SizeRatExp}}{23}{subsection.3.1.4}
\contentsline {subsection}{\numberline {3.1.5}\leavevmode {\color {Chapter }IsRationalExpression}}{23}{subsection.3.1.5}
\contentsline {subsection}{\numberline {3.1.6}\leavevmode {\color {Chapter }AlphabetOfRatExp}}{24}{subsection.3.1.6}
\contentsline {subsection}{\numberline {3.1.7}\leavevmode {\color {Chapter }AlphabetOfRatExpAsList}}{24}{subsection.3.1.7}
\contentsline {subsection}{\numberline {3.1.8}\leavevmode {\color {Chapter }CopyRatExp}}{25}{subsection.3.1.8}
\contentsline {section}{\numberline {3.2}\leavevmode {\color {Chapter }Comparison of rational expressions}}{25}{section.3.2}
\contentsline {section}{\numberline {3.3}\leavevmode {\color {Chapter }Operations with rational languages}}{25}{section.3.3}
\contentsline {subsection}{\numberline {3.3.1}\leavevmode {\color {Chapter }UnionRatExp}}{25}{subsection.3.3.1}
\contentsline {subsection}{\numberline {3.3.2}\leavevmode {\color {Chapter }ProductRatExp}}{25}{subsection.3.3.2}
\contentsline {subsection}{\numberline {3.3.3}\leavevmode {\color {Chapter } StarRatExp}}{25}{subsection.3.3.3}
\contentsline {chapter}{\numberline {4}\leavevmode {\color {Chapter }Automata \emph {versus} rational expressions}}{27}{chapter.4}
\contentsline {section}{\numberline {4.1}\leavevmode {\color {Chapter }From automata to rational expressions}}{27}{section.4.1}
\contentsline {subsection}{\numberline {4.1.1}\leavevmode {\color {Chapter }AutomatonToRatExp }}{27}{subsection.4.1.1}
\contentsline {section}{\numberline {4.2}\leavevmode {\color {Chapter }From rational expression to automata}}{27}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}\leavevmode {\color {Chapter }RatExpToNDAut}}{27}{subsection.4.2.1}
\contentsline {subsection}{\numberline {4.2.2}\leavevmode {\color {Chapter }RatExpToAutomaton}}{28}{subsection.4.2.2}
\contentsline {section}{\numberline {4.3}\leavevmode {\color {Chapter } Some tests on automata }}{28}{section.4.3}
\contentsline {subsection}{\numberline {4.3.1}\leavevmode {\color {Chapter }IsEmptyLang}}{28}{subsection.4.3.1}
\contentsline {subsection}{\numberline {4.3.2}\leavevmode {\color {Chapter }IsFullLang}}{28}{subsection.4.3.2}
\contentsline {subsection}{\numberline {4.3.3}\leavevmode {\color {Chapter }AreEqualLang}}{29}{subsection.4.3.3}
\contentsline {subsection}{\numberline {4.3.4}\leavevmode {\color {Chapter }IsContainedLang}}{29}{subsection.4.3.4}
\contentsline {subsection}{\numberline {4.3.5}\leavevmode {\color {Chapter }AreDisjointLang}}{30}{subsection.4.3.5}
\contentsline {chapter}{\numberline {5}\leavevmode {\color {Chapter }Some functions involving automata}}{31}{chapter.5}
\contentsline {section}{\numberline {5.1}\leavevmode {\color {Chapter }From one type to another}}{31}{section.5.1}
\contentsline {subsection}{\numberline {5.1.1}\leavevmode {\color {Chapter }EpsilonToNFA}}{31}{subsection.5.1.1}
\contentsline {subsection}{\numberline {5.1.2}\leavevmode {\color {Chapter }EpsilonToNFASet}}{31}{subsection.5.1.2}
\contentsline {subsection}{\numberline {5.1.3}\leavevmode {\color {Chapter }EpsilonCompactedAut}}{32}{subsection.5.1.3}
\contentsline {subsection}{\numberline {5.1.4}\leavevmode {\color {Chapter }ReducedNFA}}{32}{subsection.5.1.4}
\contentsline {subsection}{\numberline {5.1.5}\leavevmode {\color {Chapter }NFAtoDFA}}{33}{subsection.5.1.5}
\contentsline {subsection}{\numberline {5.1.6}\leavevmode {\color {Chapter }FuseSymbolsAut}}{33}{subsection.5.1.6}
\contentsline {section}{\numberline {5.2}\leavevmode {\color {Chapter }Minimalization of an automaton}}{33}{section.5.2}
\contentsline {subsection}{\numberline {5.2.1}\leavevmode {\color {Chapter }UsefulAutomaton}}{34}{subsection.5.2.1}
\contentsline {subsection}{\numberline {5.2.2}\leavevmode {\color {Chapter }MinimalizedAut}}{34}{subsection.5.2.2}
\contentsline {subsection}{\numberline {5.2.3}\leavevmode {\color {Chapter } MinimalAutomaton}}{34}{subsection.5.2.3}
\contentsline {subsection}{\numberline {5.2.4}\leavevmode {\color {Chapter }AccessibleStates}}{35}{subsection.5.2.4}
\contentsline {subsection}{\numberline {5.2.5}\leavevmode {\color {Chapter }AccessibleAutomaton}}{35}{subsection.5.2.5}
\contentsline {subsection}{\numberline {5.2.6}\leavevmode {\color {Chapter }IntersectionLanguage}}{36}{subsection.5.2.6}
\contentsline {subsection}{\numberline {5.2.7}\leavevmode {\color {Chapter }AutomatonAllPairsPaths}}{36}{subsection.5.2.7}
\contentsline {chapter}{\numberline {6}\leavevmode {\color {Chapter }Finite regular languages}}{38}{chapter.6}
\contentsline {section}{\numberline {6.1}\leavevmode {\color {Chapter }Dealing with finite regular languages}}{38}{section.6.1}
\contentsline {subsection}{\numberline {6.1.1}\leavevmode {\color {Chapter }IsFiniteRegularLanguage}}{38}{subsection.6.1.1}
\contentsline {subsection}{\numberline {6.1.2}\leavevmode {\color {Chapter }FiniteRegularLanguageToListOfWords}}{38}{subsection.6.1.2}
\contentsline {subsection}{\numberline {6.1.3}\leavevmode {\color {Chapter }ListOfWordsToAutomaton}}{38}{subsection.6.1.3}
\contentsline {chapter}{\numberline {A}\leavevmode {\color {Chapter }Directed graphs}}{40}{appendix.A}
\contentsline {section}{\numberline {A.1}\leavevmode {\color {Chapter }Directed graphs}}{40}{section.A.1}
\contentsline {subsection}{\numberline {A.1.1}\leavevmode {\color {Chapter }RandomDiGraph}}{41}{subsection.A.1.1}
\contentsline {subsection}{\numberline {A.1.2}\leavevmode {\color {Chapter }VertexInDegree}}{41}{subsection.A.1.2}
\contentsline {subsection}{\numberline {A.1.3}\leavevmode {\color {Chapter }VertexOutDegree}}{41}{subsection.A.1.3}
\contentsline {subsection}{\numberline {A.1.4}\leavevmode {\color {Chapter }AutoVertexDegree}}{41}{subsection.A.1.4}
\contentsline {subsection}{\numberline {A.1.5}\leavevmode {\color {Chapter }ReversedGraph}}{41}{subsection.A.1.5}
\contentsline {subsection}{\numberline {A.1.6}\leavevmode {\color {Chapter }AutoConnectedComponents}}{42}{subsection.A.1.6}
\contentsline {subsection}{\numberline {A.1.7}\leavevmode {\color {Chapter }GraphStronglyConnectedComponents}}{42}{subsection.A.1.7}
\contentsline {subsection}{\numberline {A.1.8}\leavevmode {\color {Chapter }UnderlyingMultiGraphOfAutomaton}}{42}{subsection.A.1.8}
\contentsline {subsection}{\numberline {A.1.9}\leavevmode {\color {Chapter }UnderlyingGraphOfAutomaton}}{43}{subsection.A.1.9}
\contentsline {subsection}{\numberline {A.1.10}\leavevmode {\color {Chapter }DiGraphToRelation}}{43}{subsection.A.1.10}
\contentsline {subsection}{\numberline {A.1.11}\leavevmode {\color {Chapter }MSccAutomaton}}{43}{subsection.A.1.11}
\contentsline {subsection}{\numberline {A.1.12}\leavevmode {\color {Chapter }AutoIsAcyclicGraph}}{44}{subsection.A.1.12}
\contentsline {chapter}{\numberline {B}\leavevmode {\color {Chapter } Drawing automata }}{45}{appendix.B}
\contentsline {section}{\numberline {B.1}\leavevmode {\color {Chapter } Installing some external programs }}{45}{section.B.1}
\contentsline {section}{\numberline {B.2}\leavevmode {\color {Chapter } Functions to draw automata }}{45}{section.B.2}
\contentsline {subsection}{\numberline {B.2.1}\leavevmode {\color {Chapter }DrawAutomaton}}{45}{subsection.B.2.1}
\contentsline {subsection}{\numberline {B.2.2}\leavevmode {\color {Chapter }DrawAutomata}}{45}{subsection.B.2.2}
\contentsline {subsection}{\numberline {B.2.3}\leavevmode {\color {Chapter }DrawGraph}}{45}{subsection.B.2.3}
\contentsline {subsection}{\numberline {B.2.4}\leavevmode {\color {Chapter }DrawSCCAutomaton}}{46}{subsection.B.2.4}
\contentsline {chapter}{\numberline {C}\leavevmode {\color {Chapter }Inverse automata and subgroups of the free group}}{47}{appendix.C}
\contentsline {section}{\numberline {C.1}\leavevmode {\color {Chapter }From subgroups to inverse automata}}{47}{section.C.1}
\contentsline {subsection}{\numberline {C.1.1}\leavevmode {\color {Chapter }GeneratorsToListRepresentation}}{47}{subsection.C.1.1}
\contentsline {subsection}{\numberline {C.1.2}\leavevmode {\color {Chapter }ListToGeneratorsRepresentation}}{47}{subsection.C.1.2}
\contentsline {subsection}{\numberline {C.1.3}\leavevmode {\color {Chapter }FlowerAutomaton}}{48}{subsection.C.1.3}
\contentsline {subsection}{\numberline {C.1.4}\leavevmode {\color {Chapter }FoldFlowerAutomaton}}{48}{subsection.C.1.4}
\contentsline {subsection}{\numberline {C.1.5}\leavevmode {\color {Chapter }SubgroupGenToInvAut}}{48}{subsection.C.1.5}
\contentsline {section}{\numberline {C.2}\leavevmode {\color {Chapter }From inverse automata to subgroups}}{49}{section.C.2}
\contentsline {subsection}{\numberline {C.2.1}\leavevmode {\color {Chapter }GeodesicTreeOfInverseAutomaton}}{49}{subsection.C.2.1}
\contentsline {subsection}{\numberline {C.2.2}\leavevmode {\color {Chapter }InverseAutomatonToGenerators}}{49}{subsection.C.2.2}
