\relax 
\ifx\hyper@anchor\@undefined
\global \let \oldcontentsline\contentsline
\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global \let \oldnewlabel\newlabel
\gdef \newlabel#1#2{\newlabelxx{#1}#2}
\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\let \contentsline\oldcontentsline
\let \newlabel\oldnewlabel}
\else
\global \let \hyper@last\relax 
\fi

\@writefile{toc}{\contentsline {chapter}{\numberline {1}\leavevmode {\color  {Chapter }Licensing}}{10}{chapter.1}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\citation{MR2091700}
\citation{MR2035113}
\@writefile{toc}{\contentsline {chapter}{\numberline {2}\leavevmode {\color  {Chapter }FR package}}{11}{chapter.2}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{frpackage}{{2}{11}{\textcolor {Chapter }{FR package}\relax }{chapter.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2.1}\leavevmode {\color  {Chapter }A brief mathematical introduction}}{11}{section.2.1}}
\newlabel{mathintro}{{2.1}{11}{\textcolor {Chapter }{A brief mathematical introduction}\relax }{section.2.1}{}}
\@writefile{brf}{\backcite{MR2091700}{{11}{2.1}{section.2.1}}}
\@writefile{brf}{\backcite{MR2035113}{{11}{2.1}{section.2.1}}}
\citation{MR713968}
\citation{MR565099}
\citation{MR696534}
\citation{MR1902367}
\citation{MR2176547}
\@writefile{brf}{\backcite{MR713968}{{12}{2.1}{section.2.1}}}
\@writefile{brf}{\backcite{MR565099}{{12}{2.1}{section.2.1}}}
\@writefile{brf}{\backcite{MR696534}{{12}{2.1}{section.2.1}}}
\@writefile{toc}{\contentsline {section}{\numberline {2.2}\leavevmode {\color  {Chapter }An example session}}{12}{section.2.2}}
\newlabel{frintro}{{2.2}{12}{\textcolor {Chapter }{An example session}\relax }{section.2.2}{}}
\@writefile{brf}{\backcite{MR1902367}{{12}{2.2}{section.2.2}}}
\@writefile{brf}{\backcite{MR2176547}{{12}{2.2}{section.2.2}}}
\@writefile{toc}{\contentsline {chapter}{\numberline {3}\leavevmode {\color  {Chapter }Functionally recursive machines}}{16}{chapter.3}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{frmachines}{{3}{16}{\textcolor {Chapter }{Functionally recursive machines}\relax }{chapter.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3.1}\leavevmode {\color  {Chapter }Types of machines}}{16}{section.3.1}}
\newlabel{frmachine-types}{{3.1}{16}{\textcolor {Chapter }{Types of machines}\relax }{section.3.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3.2}\leavevmode {\color  {Chapter }Products of machines}}{17}{section.3.2}}
\newlabel{frmachine-products}{{3.2}{17}{\textcolor {Chapter }{Products of machines}\relax }{section.3.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3.3}\leavevmode {\color  {Chapter }Creators for \texttt  {FRMachine}s}}{17}{section.3.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3.1}\leavevmode {\color  {Chapter }FRMachineNC (family,free,listlist,list)}}{17}{subsection.3.3.1}}
\newlabel{FRMachineNC:family,free,listlist,list}{{3.3.1}{17}{\textcolor {Chapter }{FRMachineNC (family,free,listlist,list)}\relax }{subsection.3.3.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3.2}\leavevmode {\color  {Chapter }FRMachine ([list,]list,list)}}{17}{subsection.3.3.2}}
\newlabel{FRMachine:[list,]list,list}{{3.3.2}{17}{\textcolor {Chapter }{FRMachine ([list,]list,list)}\relax }{subsection.3.3.2}{}}
\newlabel{FRMachine:semigroup,list,list}{{3.3.2}{17}{\textcolor {Chapter }{FRMachine ([list,]list,list)}\relax }{subsection.3.3.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3.3}\leavevmode {\color  {Chapter }UnderlyingFRMachine}}{18}{subsection.3.3.3}}
\newlabel{UnderlyingFRMachine}{{3.3.3}{18}{\textcolor {Chapter }{UnderlyingFRMachine}\relax }{subsection.3.3.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3.4}\leavevmode {\color  {Chapter }AsGroupFRMachine}}{19}{subsection.3.3.4}}
\newlabel{AsGroupFRMachine}{{3.3.4}{19}{\textcolor {Chapter }{AsGroupFRMachine}\relax }{subsection.3.3.4}{}}
\newlabel{AsMonoidFRMachine}{{3.3.4}{19}{\textcolor {Chapter }{AsGroupFRMachine}\relax }{subsection.3.3.4}{}}
\newlabel{AsSemigroupFRMachine}{{3.3.4}{19}{\textcolor {Chapter }{AsGroupFRMachine}\relax }{subsection.3.3.4}{}}
\citation{MR2162164}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3.5}\leavevmode {\color  {Chapter }ChangeFRMachineBasis}}{21}{subsection.3.3.5}}
\newlabel{ChangeFRMachineBasis}{{3.3.5}{21}{\textcolor {Chapter }{ChangeFRMachineBasis}\relax }{subsection.3.3.5}{}}
\@writefile{brf}{\backcite{MR2162164}{{21}{3.3.5}{subsection.3.3.5}}}
\@writefile{toc}{\contentsline {section}{\numberline {3.4}\leavevmode {\color  {Chapter }Attributes for \texttt  {FRMachine}s}}{21}{section.3.4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4.1}\leavevmode {\color  {Chapter }StateSet (FR machine)}}{21}{subsection.3.4.1}}
\newlabel{StateSet:FR machine}{{3.4.1}{21}{\textcolor {Chapter }{StateSet (FR machine)}\relax }{subsection.3.4.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4.2}\leavevmode {\color  {Chapter }GeneratorsOfFRMachine}}{22}{subsection.3.4.2}}
\newlabel{GeneratorsOfFRMachine}{{3.4.2}{22}{\textcolor {Chapter }{GeneratorsOfFRMachine}\relax }{subsection.3.4.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4.3}\leavevmode {\color  {Chapter }Output (FR machine,state)}}{22}{subsection.3.4.3}}
\newlabel{Output:FR machine,state}{{3.4.3}{22}{\textcolor {Chapter }{Output (FR machine,state)}\relax }{subsection.3.4.3}{}}
\newlabel{Output:FR machine,state,letter}{{3.4.3}{22}{\textcolor {Chapter }{Output (FR machine,state)}\relax }{subsection.3.4.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4.4}\leavevmode {\color  {Chapter }Transition (FR machine,state,input)}}{22}{subsection.3.4.4}}
\newlabel{Transition:FR machine,state,input}{{3.4.4}{22}{\textcolor {Chapter }{Transition (FR machine,state,input)}\relax }{subsection.3.4.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4.5}\leavevmode {\color  {Chapter }Transitions (FR machine,state)}}{22}{subsection.3.4.5}}
\newlabel{Transitions:FR machine,state}{{3.4.5}{22}{\textcolor {Chapter }{Transitions (FR machine,state)}\relax }{subsection.3.4.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4.6}\leavevmode {\color  {Chapter }WreathRecursion}}{23}{subsection.3.4.6}}
\newlabel{WreathRecursion}{{3.4.6}{23}{\textcolor {Chapter }{WreathRecursion}\relax }{subsection.3.4.6}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3.5}\leavevmode {\color  {Chapter }Operations for \texttt  {FRMachine}s}}{23}{section.3.5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.5.1}\leavevmode {\color  {Chapter }StructuralGroup}}{23}{subsection.3.5.1}}
\newlabel{StructuralGroup}{{3.5.1}{23}{\textcolor {Chapter }{StructuralGroup}\relax }{subsection.3.5.1}{}}
\newlabel{StructuralMonoid}{{3.5.1}{23}{\textcolor {Chapter }{StructuralGroup}\relax }{subsection.3.5.1}{}}
\newlabel{StructuralSemigroup}{{3.5.1}{23}{\textcolor {Chapter }{StructuralGroup}\relax }{subsection.3.5.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.5.2}\leavevmode {\color  {Chapter }\texttt  {\char 92\relax }+}}{24}{subsection.3.5.2}}
\newlabel{+}{{3.5.2}{24}{\textcolor {Chapter }{\texttt {\symbol {92}}+}\relax }{subsection.3.5.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.5.3}\leavevmode {\color  {Chapter }\texttt  {\char 92\relax }*}}{24}{subsection.3.5.3}}
\newlabel{*}{{3.5.3}{24}{\textcolor {Chapter }{\texttt {\symbol {92}}*}\relax }{subsection.3.5.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.5.4}\leavevmode {\color  {Chapter }TensorSumOp (FR Machines)}}{24}{subsection.3.5.4}}
\newlabel{TensorSumOp:FR Machines}{{3.5.4}{24}{\textcolor {Chapter }{TensorSumOp (FR Machines)}\relax }{subsection.3.5.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.5.5}\leavevmode {\color  {Chapter }TensorProductOp (FR Machines)}}{25}{subsection.3.5.5}}
\newlabel{TensorProductOp:FR Machines}{{3.5.5}{25}{\textcolor {Chapter }{TensorProductOp (FR Machines)}\relax }{subsection.3.5.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.5.6}\leavevmode {\color  {Chapter }DirectSumOp (FR Machines)}}{25}{subsection.3.5.6}}
\newlabel{DirectSumOp:FR Machines}{{3.5.6}{25}{\textcolor {Chapter }{DirectSumOp (FR Machines)}\relax }{subsection.3.5.6}{}}
\citation{MR2197828}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.5.7}\leavevmode {\color  {Chapter }DirectProductOp (FR Machines)}}{26}{subsection.3.5.7}}
\newlabel{DirectProductOp:FR Machines}{{3.5.7}{26}{\textcolor {Chapter }{DirectProductOp (FR Machines)}\relax }{subsection.3.5.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.5.8}\leavevmode {\color  {Chapter }TreeWreathProduct (FR machine)}}{26}{subsection.3.5.8}}
\newlabel{TreeWreathProduct:FR machine}{{3.5.8}{26}{\textcolor {Chapter }{TreeWreathProduct (FR machine)}\relax }{subsection.3.5.8}{}}
\@writefile{brf}{\backcite{MR2197828}{{26}{3.5.8}{subsection.3.5.8}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.5.9}\leavevmode {\color  {Chapter }SubFRMachine}}{27}{subsection.3.5.9}}
\newlabel{SubFRMachine}{{3.5.9}{27}{\textcolor {Chapter }{SubFRMachine}\relax }{subsection.3.5.9}{}}
\newlabel{SubFRMachine:machine,map}{{3.5.9}{27}{\textcolor {Chapter }{SubFRMachine}\relax }{subsection.3.5.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.5.10}\leavevmode {\color  {Chapter }Minimized (FR machine)}}{27}{subsection.3.5.10}}
\newlabel{Minimized:FR machine}{{3.5.10}{27}{\textcolor {Chapter }{Minimized (FR machine)}\relax }{subsection.3.5.10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.5.11}\leavevmode {\color  {Chapter }Correspondence (FR machine)}}{27}{subsection.3.5.11}}
\newlabel{Correspondence:FR machine}{{3.5.11}{27}{\textcolor {Chapter }{Correspondence (FR machine)}\relax }{subsection.3.5.11}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {4}\leavevmode {\color  {Chapter }Functionally recursive elements}}{29}{chapter.4}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{frelements}{{4}{29}{\textcolor {Chapter }{Functionally recursive elements}\relax }{chapter.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4.1}\leavevmode {\color  {Chapter }Creators for \texttt  {FRElement}s}}{29}{section.4.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.1}\leavevmode {\color  {Chapter }FRElementNC (family,free,listlist,list,assocword)}}{29}{subsection.4.1.1}}
\newlabel{FRElementNC:family,free,listlist,list,assocword}{{4.1.1}{29}{\textcolor {Chapter }{FRElementNC (family,free,listlist,list,assocword)}\relax }{subsection.4.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.2}\leavevmode {\color  {Chapter }FRElement ([list,]list,list,list)}}{30}{subsection.4.1.2}}
\newlabel{FRElement:[list,]list,list,list}{{4.1.2}{30}{\textcolor {Chapter }{FRElement ([list,]list,list,list)}\relax }{subsection.4.1.2}{}}
\newlabel{FRElement:semigroup,list,list,list}{{4.1.2}{30}{\textcolor {Chapter }{FRElement ([list,]list,list,list)}\relax }{subsection.4.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.3}\leavevmode {\color  {Chapter }FRElement (machine/element,list)}}{31}{subsection.4.1.3}}
\newlabel{FRElement:machine/element,list}{{4.1.3}{31}{\textcolor {Chapter }{FRElement (machine/element,list)}\relax }{subsection.4.1.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.4}\leavevmode {\color  {Chapter }ComposeElement (elementcoll,perm)}}{31}{subsection.4.1.4}}
\newlabel{ComposeElement:elementcoll,perm}{{4.1.4}{31}{\textcolor {Chapter }{ComposeElement (elementcoll,perm)}\relax }{subsection.4.1.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.5}\leavevmode {\color  {Chapter }VertexElement}}{32}{subsection.4.1.5}}
\newlabel{VertexElement}{{4.1.5}{32}{\textcolor {Chapter }{VertexElement}\relax }{subsection.4.1.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.6}\leavevmode {\color  {Chapter }DiagonalElement}}{32}{subsection.4.1.6}}
\newlabel{DiagonalElement}{{4.1.6}{32}{\textcolor {Chapter }{DiagonalElement}\relax }{subsection.4.1.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.7}\leavevmode {\color  {Chapter }AsGroupFRElement}}{33}{subsection.4.1.7}}
\newlabel{AsGroupFRElement}{{4.1.7}{33}{\textcolor {Chapter }{AsGroupFRElement}\relax }{subsection.4.1.7}{}}
\newlabel{AsMonoidFRElement}{{4.1.7}{33}{\textcolor {Chapter }{AsGroupFRElement}\relax }{subsection.4.1.7}{}}
\newlabel{AsSemigroupFRElement}{{4.1.7}{33}{\textcolor {Chapter }{AsGroupFRElement}\relax }{subsection.4.1.7}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4.2}\leavevmode {\color  {Chapter }Operations and Attributes for \texttt  {FRElement}s}}{34}{section.4.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.1}\leavevmode {\color  {Chapter }Output (FR element)}}{34}{subsection.4.2.1}}
\newlabel{Output:FR element}{{4.2.1}{34}{\textcolor {Chapter }{Output (FR element)}\relax }{subsection.4.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.2}\leavevmode {\color  {Chapter }Activity}}{35}{subsection.4.2.2}}
\newlabel{Activity}{{4.2.2}{35}{\textcolor {Chapter }{Activity}\relax }{subsection.4.2.2}{}}
\newlabel{ActivityInt}{{4.2.2}{35}{\textcolor {Chapter }{Activity}\relax }{subsection.4.2.2}{}}
\newlabel{ActivityTransformation}{{4.2.2}{35}{\textcolor {Chapter }{Activity}\relax }{subsection.4.2.2}{}}
\newlabel{ActivityPerm}{{4.2.2}{35}{\textcolor {Chapter }{Activity}\relax }{subsection.4.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.3}\leavevmode {\color  {Chapter }Transition (FR element,input)}}{35}{subsection.4.2.3}}
\newlabel{Transition:FR element,input}{{4.2.3}{35}{\textcolor {Chapter }{Transition (FR element,input)}\relax }{subsection.4.2.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.4}\leavevmode {\color  {Chapter }Transitions (FR element)}}{36}{subsection.4.2.4}}
\newlabel{Transitions:FR element}{{4.2.4}{36}{\textcolor {Chapter }{Transitions (FR element)}\relax }{subsection.4.2.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.5}\leavevmode {\color  {Chapter }Portrait}}{36}{subsection.4.2.5}}
\newlabel{Portrait}{{4.2.5}{36}{\textcolor {Chapter }{Portrait}\relax }{subsection.4.2.5}{}}
\newlabel{PortraitPerm}{{4.2.5}{36}{\textcolor {Chapter }{Portrait}\relax }{subsection.4.2.5}{}}
\newlabel{PortraitInt}{{4.2.5}{36}{\textcolor {Chapter }{Portrait}\relax }{subsection.4.2.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.6}\leavevmode {\color  {Chapter }DecompositionOfFRElement}}{36}{subsection.4.2.6}}
\newlabel{DecompositionOfFRElement}{{4.2.6}{36}{\textcolor {Chapter }{DecompositionOfFRElement}\relax }{subsection.4.2.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.7}\leavevmode {\color  {Chapter }StateSet (FR element)}}{37}{subsection.4.2.7}}
\newlabel{StateSet:FR element}{{4.2.7}{37}{\textcolor {Chapter }{StateSet (FR element)}\relax }{subsection.4.2.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.8}\leavevmode {\color  {Chapter }State}}{37}{subsection.4.2.8}}
\newlabel{State}{{4.2.8}{37}{\textcolor {Chapter }{State}\relax }{subsection.4.2.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.9}\leavevmode {\color  {Chapter }States}}{37}{subsection.4.2.9}}
\newlabel{States}{{4.2.9}{37}{\textcolor {Chapter }{States}\relax }{subsection.4.2.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.10}\leavevmode {\color  {Chapter }FixedStates}}{38}{subsection.4.2.10}}
\newlabel{FixedStates}{{4.2.10}{38}{\textcolor {Chapter }{FixedStates}\relax }{subsection.4.2.10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.11}\leavevmode {\color  {Chapter }LimitStates}}{38}{subsection.4.2.11}}
\newlabel{LimitStates}{{4.2.11}{38}{\textcolor {Chapter }{LimitStates}\relax }{subsection.4.2.11}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.12}\leavevmode {\color  {Chapter }IsFiniteStateFRElement}}{39}{subsection.4.2.12}}
\newlabel{IsFiniteStateFRElement}{{4.2.12}{39}{\textcolor {Chapter }{IsFiniteStateFRElement}\relax }{subsection.4.2.12}{}}
\newlabel{IsFiniteStateFRMachine}{{4.2.12}{39}{\textcolor {Chapter }{IsFiniteStateFRElement}\relax }{subsection.4.2.12}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.13}\leavevmode {\color  {Chapter }NucleusOfFRMachine}}{39}{subsection.4.2.13}}
\newlabel{NucleusOfFRMachine}{{4.2.13}{39}{\textcolor {Chapter }{NucleusOfFRMachine}\relax }{subsection.4.2.13}{}}
\newlabel{Nucleus:FR machine}{{4.2.13}{39}{\textcolor {Chapter }{NucleusOfFRMachine}\relax }{subsection.4.2.13}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.14}\leavevmode {\color  {Chapter }InitialState}}{40}{subsection.4.2.14}}
\newlabel{InitialState}{{4.2.14}{40}{\textcolor {Chapter }{InitialState}\relax }{subsection.4.2.14}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.15}\leavevmode {\color  {Chapter }\texttt  {\char 92\relax }\texttt  {\char 94\relax } (POW)}}{40}{subsection.4.2.15}}
\newlabel{^:POW}{{4.2.15}{40}{\textcolor {Chapter }{\texttt {\symbol {92}}\texttt {\symbol {94}} (POW)}\relax }{subsection.4.2.15}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.16}\leavevmode {\color  {Chapter }\texttt  {\char 92\relax }* (PROD)}}{40}{subsection.4.2.16}}
\newlabel{*:PROD}{{4.2.16}{40}{\textcolor {Chapter }{\texttt {\symbol {92}}* (PROD)}\relax }{subsection.4.2.16}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.17}\leavevmode {\color  {Chapter }\texttt  {\char 92\relax }[\texttt  {\char 92\relax }] (ELMLIST)}}{41}{subsection.4.2.17}}
\newlabel{[]:ELMLIST}{{4.2.17}{41}{\textcolor {Chapter }{\texttt {\symbol {92}}[\texttt {\symbol {92}}] (ELMLIST)}\relax }{subsection.4.2.17}{}}
\newlabel{{}:ELMSLIST}{{4.2.17}{41}{\textcolor {Chapter }{\texttt {\symbol {92}}[\texttt {\symbol {92}}] (ELMLIST)}\relax }{subsection.4.2.17}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {5}\leavevmode {\color  {Chapter }Mealy machines and elements}}{42}{chapter.5}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{mealy}{{5}{42}{\textcolor {Chapter }{Mealy machines and elements}\relax }{chapter.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5.1}\leavevmode {\color  {Chapter }Creators for \texttt  {MealyMachine}s and \texttt  {MealyElement}s}}{42}{section.5.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.1.1}\leavevmode {\color  {Chapter }MealyMachine ([list,]listlist,list)}}{42}{subsection.5.1.1}}
\newlabel{MealyMachine:[list,]listlist,list}{{5.1.1}{42}{\textcolor {Chapter }{MealyMachine ([list,]listlist,list)}\relax }{subsection.5.1.1}{}}
\newlabel{MealyElement:[list,]listlist,list,int}{{5.1.1}{42}{\textcolor {Chapter }{MealyMachine ([list,]listlist,list)}\relax }{subsection.5.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.1.2}\leavevmode {\color  {Chapter }MealyMachine (domain,domain,function,function)}}{43}{subsection.5.1.2}}
\newlabel{MealyMachine:domain,domain,function,function}{{5.1.2}{43}{\textcolor {Chapter }{MealyMachine (domain,domain,function,function)}\relax }{subsection.5.1.2}{}}
\newlabel{MealyElement:domain,domain,function,function,obj}{{5.1.2}{43}{\textcolor {Chapter }{MealyMachine (domain,domain,function,function)}\relax }{subsection.5.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.1.3}\leavevmode {\color  {Chapter }MealyMachineNC (family,listlist,list)}}{44}{subsection.5.1.3}}
\newlabel{MealyMachineNC:family,listlist,list}{{5.1.3}{44}{\textcolor {Chapter }{MealyMachineNC (family,listlist,list)}\relax }{subsection.5.1.3}{}}
\newlabel{MealyElementNC:family,listlist,list,int}{{5.1.3}{44}{\textcolor {Chapter }{MealyMachineNC (family,listlist,list)}\relax }{subsection.5.1.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.1.4}\leavevmode {\color  {Chapter }AllMealyMachines}}{44}{subsection.5.1.4}}
\newlabel{AllMealyMachines}{{5.1.4}{44}{\textcolor {Chapter }{AllMealyMachines}\relax }{subsection.5.1.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5.2}\leavevmode {\color  {Chapter }Operations and Attributes for \texttt  {MealyMachine}s and \texttt  {MealyElement}s}}{45}{section.5.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.1}\leavevmode {\color  {Chapter }Draw}}{45}{subsection.5.2.1}}
\newlabel{Draw}{{5.2.1}{45}{\textcolor {Chapter }{Draw}\relax }{subsection.5.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.2}\leavevmode {\color  {Chapter }Minimized (Mealy machine)}}{46}{subsection.5.2.2}}
\newlabel{Minimized:Mealy machine}{{5.2.2}{46}{\textcolor {Chapter }{Minimized (Mealy machine)}\relax }{subsection.5.2.2}{}}
\citation{MR1841119}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.3}\leavevmode {\color  {Chapter }DualMachine}}{47}{subsection.5.2.3}}
\newlabel{DualMachine}{{5.2.3}{47}{\textcolor {Chapter }{DualMachine}\relax }{subsection.5.2.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.4}\leavevmode {\color  {Chapter }IsReversible}}{47}{subsection.5.2.4}}
\newlabel{IsReversible}{{5.2.4}{47}{\textcolor {Chapter }{IsReversible}\relax }{subsection.5.2.4}{}}
\@writefile{brf}{\backcite{MR1841119}{{47}{5.2.4}{subsection.5.2.4}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.5}\leavevmode {\color  {Chapter }IsMinimized}}{47}{subsection.5.2.5}}
\newlabel{IsMinimized}{{5.2.5}{47}{\textcolor {Chapter }{IsMinimized}\relax }{subsection.5.2.5}{}}
\citation{MR1841119}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.6}\leavevmode {\color  {Chapter }AlphabetInvolution}}{48}{subsection.5.2.6}}
\newlabel{AlphabetInvolution}{{5.2.6}{48}{\textcolor {Chapter }{AlphabetInvolution}\relax }{subsection.5.2.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.7}\leavevmode {\color  {Chapter }IsBireversible}}{48}{subsection.5.2.7}}
\newlabel{IsBireversible}{{5.2.7}{48}{\textcolor {Chapter }{IsBireversible}\relax }{subsection.5.2.7}{}}
\@writefile{brf}{\backcite{MR1841119}{{48}{5.2.7}{subsection.5.2.7}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.8}\leavevmode {\color  {Chapter }StateGrowth}}{48}{subsection.5.2.8}}
\newlabel{StateGrowth}{{5.2.8}{48}{\textcolor {Chapter }{StateGrowth}\relax }{subsection.5.2.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.9}\leavevmode {\color  {Chapter }Degree (FR element)}}{48}{subsection.5.2.9}}
\newlabel{Degree:FR element}{{5.2.9}{48}{\textcolor {Chapter }{Degree (FR element)}\relax }{subsection.5.2.9}{}}
\newlabel{DegreeOfFRMachine}{{5.2.9}{48}{\textcolor {Chapter }{Degree (FR element)}\relax }{subsection.5.2.9}{}}
\newlabel{DegreeOfFRElement}{{5.2.9}{48}{\textcolor {Chapter }{Degree (FR element)}\relax }{subsection.5.2.9}{}}
\citation{MR1774362}
\@writefile{brf}{\backcite{MR1774362}{{49}{5.2.9}{subsection.5.2.9}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.10}\leavevmode {\color  {Chapter }IsFinitaryFRElement}}{49}{subsection.5.2.10}}
\newlabel{IsFinitaryFRElement}{{5.2.10}{49}{\textcolor {Chapter }{IsFinitaryFRElement}\relax }{subsection.5.2.10}{}}
\newlabel{IsFinitaryFRMachine}{{5.2.10}{49}{\textcolor {Chapter }{IsFinitaryFRElement}\relax }{subsection.5.2.10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.11}\leavevmode {\color  {Chapter }Depth (FR element)}}{49}{subsection.5.2.11}}
\newlabel{Depth:FR element}{{5.2.11}{49}{\textcolor {Chapter }{Depth (FR element)}\relax }{subsection.5.2.11}{}}
\newlabel{DepthOfFRMachine}{{5.2.11}{49}{\textcolor {Chapter }{Depth (FR element)}\relax }{subsection.5.2.11}{}}
\newlabel{DepthOfFRElement}{{5.2.11}{49}{\textcolor {Chapter }{Depth (FR element)}\relax }{subsection.5.2.11}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.12}\leavevmode {\color  {Chapter }IsBoundedFRElement}}{50}{subsection.5.2.12}}
\newlabel{IsBoundedFRElement}{{5.2.12}{50}{\textcolor {Chapter }{IsBoundedFRElement}\relax }{subsection.5.2.12}{}}
\newlabel{IsBoundedFRMachine}{{5.2.12}{50}{\textcolor {Chapter }{IsBoundedFRElement}\relax }{subsection.5.2.12}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.13}\leavevmode {\color  {Chapter }IsPolynomialGrowthFRElement}}{50}{subsection.5.2.13}}
\newlabel{IsPolynomialGrowthFRElement}{{5.2.13}{50}{\textcolor {Chapter }{IsPolynomialGrowthFRElement}\relax }{subsection.5.2.13}{}}
\newlabel{IsPolynomialGrowthFRMachine}{{5.2.13}{50}{\textcolor {Chapter }{IsPolynomialGrowthFRElement}\relax }{subsection.5.2.13}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.14}\leavevmode {\color  {Chapter }Signatures}}{51}{subsection.5.2.14}}
\newlabel{Signatures}{{5.2.14}{51}{\textcolor {Chapter }{Signatures}\relax }{subsection.5.2.14}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.15}\leavevmode {\color  {Chapter }VertexTransformationsFRMachine}}{51}{subsection.5.2.15}}
\newlabel{VertexTransformationsFRMachine}{{5.2.15}{51}{\textcolor {Chapter }{VertexTransformationsFRMachine}\relax }{subsection.5.2.15}{}}
\newlabel{VertexTransformationsFRElement}{{5.2.15}{51}{\textcolor {Chapter }{VertexTransformationsFRMachine}\relax }{subsection.5.2.15}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.16}\leavevmode {\color  {Chapter }FixedRay (FR element)}}{51}{subsection.5.2.16}}
\newlabel{FixedRay:FR element}{{5.2.16}{51}{\textcolor {Chapter }{FixedRay (FR element)}\relax }{subsection.5.2.16}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.17}\leavevmode {\color  {Chapter }IsLevelTransitive (FR element)}}{52}{subsection.5.2.17}}
\newlabel{IsLevelTransitive:FR element}{{5.2.17}{52}{\textcolor {Chapter }{IsLevelTransitive (FR element)}\relax }{subsection.5.2.17}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.18}\leavevmode {\color  {Chapter }AsMealyMachine (FR machine)}}{52}{subsection.5.2.18}}
\newlabel{AsMealyMachine:FR machine}{{5.2.18}{52}{\textcolor {Chapter }{AsMealyMachine (FR machine)}\relax }{subsection.5.2.18}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.19}\leavevmode {\color  {Chapter }AsMealyMachine (List)}}{53}{subsection.5.2.19}}
\newlabel{AsMealyMachine:List}{{5.2.19}{53}{\textcolor {Chapter }{AsMealyMachine (List)}\relax }{subsection.5.2.19}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.20}\leavevmode {\color  {Chapter }AsMealyElement}}{53}{subsection.5.2.20}}
\newlabel{AsMealyElement}{{5.2.20}{53}{\textcolor {Chapter }{AsMealyElement}\relax }{subsection.5.2.20}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.21}\leavevmode {\color  {Chapter }AsIntMealyMachine}}{54}{subsection.5.2.21}}
\newlabel{AsIntMealyMachine}{{5.2.21}{54}{\textcolor {Chapter }{AsIntMealyMachine}\relax }{subsection.5.2.21}{}}
\newlabel{AsIntMealyElement}{{5.2.21}{54}{\textcolor {Chapter }{AsIntMealyMachine}\relax }{subsection.5.2.21}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.22}\leavevmode {\color  {Chapter }TopElement}}{54}{subsection.5.2.22}}
\newlabel{TopElement}{{5.2.22}{54}{\textcolor {Chapter }{TopElement}\relax }{subsection.5.2.22}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.23}\leavevmode {\color  {Chapter }ConfinalityClasses}}{54}{subsection.5.2.23}}
\newlabel{ConfinalityClasses}{{5.2.23}{54}{\textcolor {Chapter }{ConfinalityClasses}\relax }{subsection.5.2.23}{}}
\newlabel{IsWeaklyFinitaryFRElement}{{5.2.23}{54}{\textcolor {Chapter }{ConfinalityClasses}\relax }{subsection.5.2.23}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.24}\leavevmode {\color  {Chapter }Germs}}{55}{subsection.5.2.24}}
\newlabel{Germs}{{5.2.24}{55}{\textcolor {Chapter }{Germs}\relax }{subsection.5.2.24}{}}
\newlabel{NormOfBoundedFRElement}{{5.2.24}{55}{\textcolor {Chapter }{Germs}\relax }{subsection.5.2.24}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.25}\leavevmode {\color  {Chapter }HasOpenSetConditionFRElement}}{56}{subsection.5.2.25}}
\newlabel{HasOpenSetConditionFRElement}{{5.2.25}{56}{\textcolor {Chapter }{HasOpenSetConditionFRElement}\relax }{subsection.5.2.25}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.26}\leavevmode {\color  {Chapter }LimitMachine}}{56}{subsection.5.2.26}}
\newlabel{LimitMachine}{{5.2.26}{56}{\textcolor {Chapter }{LimitMachine}\relax }{subsection.5.2.26}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.27}\leavevmode {\color  {Chapter }NucleusMachine (FR machine)}}{56}{subsection.5.2.27}}
\newlabel{NucleusMachine:FR machine}{{5.2.27}{56}{\textcolor {Chapter }{NucleusMachine (FR machine)}\relax }{subsection.5.2.27}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.28}\leavevmode {\color  {Chapter }GuessMealyElement}}{57}{subsection.5.2.28}}
\newlabel{GuessMealyElement}{{5.2.28}{57}{\textcolor {Chapter }{GuessMealyElement}\relax }{subsection.5.2.28}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {6}\leavevmode {\color  {Chapter }Linear machines and elements}}{58}{chapter.6}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{vector}{{6}{58}{\textcolor {Chapter }{Linear machines and elements}\relax }{chapter.6}{}}
\@writefile{toc}{\contentsline {section}{\numberline {6.1}\leavevmode {\color  {Chapter }Methods and operations for \texttt  {LinearFRMachine}s and \texttt  {LinearFRElement}s}}{58}{section.6.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.1}\leavevmode {\color  {Chapter }VectorMachine}}{58}{subsection.6.1.1}}
\newlabel{VectorMachine}{{6.1.1}{58}{\textcolor {Chapter }{VectorMachine}\relax }{subsection.6.1.1}{}}
\newlabel{VectorElement}{{6.1.1}{58}{\textcolor {Chapter }{VectorMachine}\relax }{subsection.6.1.1}{}}
\newlabel{VectorMachineNC}{{6.1.1}{58}{\textcolor {Chapter }{VectorMachine}\relax }{subsection.6.1.1}{}}
\newlabel{VectorElementNC}{{6.1.1}{58}{\textcolor {Chapter }{VectorMachine}\relax }{subsection.6.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.2}\leavevmode {\color  {Chapter }AlgebraMachine}}{59}{subsection.6.1.2}}
\newlabel{AlgebraMachine}{{6.1.2}{59}{\textcolor {Chapter }{AlgebraMachine}\relax }{subsection.6.1.2}{}}
\newlabel{AlgebraElement}{{6.1.2}{59}{\textcolor {Chapter }{AlgebraMachine}\relax }{subsection.6.1.2}{}}
\newlabel{AlgebraMachineNC}{{6.1.2}{59}{\textcolor {Chapter }{AlgebraMachine}\relax }{subsection.6.1.2}{}}
\newlabel{AlgebraElementNC}{{6.1.2}{59}{\textcolor {Chapter }{AlgebraMachine}\relax }{subsection.6.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.3}\leavevmode {\color  {Chapter }Transition (Linear machine)}}{60}{subsection.6.1.3}}
\newlabel{Transition:Linear machine}{{6.1.3}{60}{\textcolor {Chapter }{Transition (Linear machine)}\relax }{subsection.6.1.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.4}\leavevmode {\color  {Chapter }Transitions}}{60}{subsection.6.1.4}}
\newlabel{Transitions}{{6.1.4}{60}{\textcolor {Chapter }{Transitions}\relax }{subsection.6.1.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.5}\leavevmode {\color  {Chapter }NestedMatrixState}}{61}{subsection.6.1.5}}
\newlabel{NestedMatrixState}{{6.1.5}{61}{\textcolor {Chapter }{NestedMatrixState}\relax }{subsection.6.1.5}{}}
\newlabel{NestedMatrixCoefficient}{{6.1.5}{61}{\textcolor {Chapter }{NestedMatrixState}\relax }{subsection.6.1.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.6}\leavevmode {\color  {Chapter }ActivitySparse}}{61}{subsection.6.1.6}}
\newlabel{ActivitySparse}{{6.1.6}{61}{\textcolor {Chapter }{ActivitySparse}\relax }{subsection.6.1.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.7}\leavevmode {\color  {Chapter }Activities}}{62}{subsection.6.1.7}}
\newlabel{Activities}{{6.1.7}{62}{\textcolor {Chapter }{Activities}\relax }{subsection.6.1.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.8}\leavevmode {\color  {Chapter }IsConvergent}}{62}{subsection.6.1.8}}
\newlabel{IsConvergent}{{6.1.8}{62}{\textcolor {Chapter }{IsConvergent}\relax }{subsection.6.1.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.9}\leavevmode {\color  {Chapter }TransposedFRElement}}{62}{subsection.6.1.9}}
\newlabel{TransposedFRElement}{{6.1.9}{62}{\textcolor {Chapter }{TransposedFRElement}\relax }{subsection.6.1.9}{}}
\newlabel{IsSymmetricFRElement}{{6.1.9}{62}{\textcolor {Chapter }{TransposedFRElement}\relax }{subsection.6.1.9}{}}
\newlabel{IsAntisymmetricFRElement}{{6.1.9}{62}{\textcolor {Chapter }{TransposedFRElement}\relax }{subsection.6.1.9}{}}
\newlabel{IsLowerTriangularFRElement}{{6.1.9}{62}{\textcolor {Chapter }{TransposedFRElement}\relax }{subsection.6.1.9}{}}
\newlabel{IsUpperTriangularFRElement}{{6.1.9}{62}{\textcolor {Chapter }{TransposedFRElement}\relax }{subsection.6.1.9}{}}
\newlabel{IsDiagonalFRElement}{{6.1.9}{62}{\textcolor {Chapter }{TransposedFRElement}\relax }{subsection.6.1.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.10}\leavevmode {\color  {Chapter }LDUDecompositionFRElement}}{63}{subsection.6.1.10}}
\newlabel{LDUDecompositionFRElement}{{6.1.10}{63}{\textcolor {Chapter }{LDUDecompositionFRElement}\relax }{subsection.6.1.10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.11}\leavevmode {\color  {Chapter }GuessVectorElement}}{64}{subsection.6.1.11}}
\newlabel{GuessVectorElement}{{6.1.11}{64}{\textcolor {Chapter }{GuessVectorElement}\relax }{subsection.6.1.11}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.12}\leavevmode {\color  {Chapter }AsLinearMachine}}{64}{subsection.6.1.12}}
\newlabel{AsLinearMachine}{{6.1.12}{64}{\textcolor {Chapter }{AsLinearMachine}\relax }{subsection.6.1.12}{}}
\newlabel{AsLinearElement}{{6.1.12}{64}{\textcolor {Chapter }{AsLinearMachine}\relax }{subsection.6.1.12}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.13}\leavevmode {\color  {Chapter }AsVectorMachine}}{65}{subsection.6.1.13}}
\newlabel{AsVectorMachine}{{6.1.13}{65}{\textcolor {Chapter }{AsVectorMachine}\relax }{subsection.6.1.13}{}}
\newlabel{AsVectorElement}{{6.1.13}{65}{\textcolor {Chapter }{AsVectorMachine}\relax }{subsection.6.1.13}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.14}\leavevmode {\color  {Chapter }AsAlgebraMachine}}{65}{subsection.6.1.14}}
\newlabel{AsAlgebraMachine}{{6.1.14}{65}{\textcolor {Chapter }{AsAlgebraMachine}\relax }{subsection.6.1.14}{}}
\newlabel{AsAlgebraElement}{{6.1.14}{65}{\textcolor {Chapter }{AsAlgebraMachine}\relax }{subsection.6.1.14}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.15}\leavevmode {\color  {Chapter }AsVectorMachine (Linear machine)}}{66}{subsection.6.1.15}}
\newlabel{AsVectorMachine:Linear machine}{{6.1.15}{66}{\textcolor {Chapter }{AsVectorMachine (Linear machine)}\relax }{subsection.6.1.15}{}}
\newlabel{AsVectorElement:Linear machine}{{6.1.15}{66}{\textcolor {Chapter }{AsVectorMachine (Linear machine)}\relax }{subsection.6.1.15}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.16}\leavevmode {\color  {Chapter }AsAlgebraMachine (Linear machine)}}{66}{subsection.6.1.16}}
\newlabel{AsAlgebraMachine:Linear machine}{{6.1.16}{66}{\textcolor {Chapter }{AsAlgebraMachine (Linear machine)}\relax }{subsection.6.1.16}{}}
\newlabel{AsAlgebraElement:Linear machine}{{6.1.16}{66}{\textcolor {Chapter }{AsAlgebraMachine (Linear machine)}\relax }{subsection.6.1.16}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {7}\leavevmode {\color  {Chapter }Self-similar groups, monoids and semigroups}}{67}{chapter.7}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{group}{{7}{67}{\textcolor {Chapter }{Self-similar groups, monoids and semigroups}\relax }{chapter.7}{}}
\@writefile{toc}{\contentsline {section}{\numberline {7.1}\leavevmode {\color  {Chapter }Creators for FR semigroups}}{67}{section.7.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.1.1}\leavevmode {\color  {Chapter }FRGroup}}{67}{subsection.7.1.1}}
\newlabel{FRGroup}{{7.1.1}{67}{\textcolor {Chapter }{FRGroup}\relax }{subsection.7.1.1}{}}
\newlabel{FRMonoid}{{7.1.1}{67}{\textcolor {Chapter }{FRGroup}\relax }{subsection.7.1.1}{}}
\newlabel{FRSemigroup}{{7.1.1}{67}{\textcolor {Chapter }{FRGroup}\relax }{subsection.7.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.1.2}\leavevmode {\color  {Chapter }SCGroup}}{69}{subsection.7.1.2}}
\newlabel{SCGroup}{{7.1.2}{69}{\textcolor {Chapter }{SCGroup}\relax }{subsection.7.1.2}{}}
\newlabel{SCGroupNC}{{7.1.2}{69}{\textcolor {Chapter }{SCGroup}\relax }{subsection.7.1.2}{}}
\newlabel{SCMonoid}{{7.1.2}{69}{\textcolor {Chapter }{SCGroup}\relax }{subsection.7.1.2}{}}
\newlabel{SCMonoidNC}{{7.1.2}{69}{\textcolor {Chapter }{SCGroup}\relax }{subsection.7.1.2}{}}
\newlabel{SCSemigroup}{{7.1.2}{69}{\textcolor {Chapter }{SCGroup}\relax }{subsection.7.1.2}{}}
\newlabel{SCSemigroupNC}{{7.1.2}{69}{\textcolor {Chapter }{SCGroup}\relax }{subsection.7.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.1.3}\leavevmode {\color  {Chapter }Correspondence (FR semigroup)}}{70}{subsection.7.1.3}}
\newlabel{Correspondence:FR semigroup}{{7.1.3}{70}{\textcolor {Chapter }{Correspondence (FR semigroup)}\relax }{subsection.7.1.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.1.4}\leavevmode {\color  {Chapter }FullSCGroup}}{70}{subsection.7.1.4}}
\newlabel{FullSCGroup}{{7.1.4}{70}{\textcolor {Chapter }{FullSCGroup}\relax }{subsection.7.1.4}{}}
\newlabel{FullSCMonoid}{{7.1.4}{70}{\textcolor {Chapter }{FullSCGroup}\relax }{subsection.7.1.4}{}}
\newlabel{FullSCSemigroup}{{7.1.4}{70}{\textcolor {Chapter }{FullSCGroup}\relax }{subsection.7.1.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.1.5}\leavevmode {\color  {Chapter }FRMachineFRGroup}}{71}{subsection.7.1.5}}
\newlabel{FRMachineFRGroup}{{7.1.5}{71}{\textcolor {Chapter }{FRMachineFRGroup}\relax }{subsection.7.1.5}{}}
\newlabel{FRMachineFRMonoid}{{7.1.5}{71}{\textcolor {Chapter }{FRMachineFRGroup}\relax }{subsection.7.1.5}{}}
\newlabel{FRMachineFRSemigroup}{{7.1.5}{71}{\textcolor {Chapter }{FRMachineFRGroup}\relax }{subsection.7.1.5}{}}
\newlabel{MealyMachineFRGroup}{{7.1.5}{71}{\textcolor {Chapter }{FRMachineFRGroup}\relax }{subsection.7.1.5}{}}
\newlabel{MealyMachineFRMonoid}{{7.1.5}{71}{\textcolor {Chapter }{FRMachineFRGroup}\relax }{subsection.7.1.5}{}}
\newlabel{MealyMachineFRSemigroup}{{7.1.5}{71}{\textcolor {Chapter }{FRMachineFRGroup}\relax }{subsection.7.1.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.1.6}\leavevmode {\color  {Chapter }IsomorphismFRGroup}}{72}{subsection.7.1.6}}
\newlabel{IsomorphismFRGroup}{{7.1.6}{72}{\textcolor {Chapter }{IsomorphismFRGroup}\relax }{subsection.7.1.6}{}}
\newlabel{IsomorphismFRMonoid}{{7.1.6}{72}{\textcolor {Chapter }{IsomorphismFRGroup}\relax }{subsection.7.1.6}{}}
\newlabel{IsomorphismFRSemigroup}{{7.1.6}{72}{\textcolor {Chapter }{IsomorphismFRGroup}\relax }{subsection.7.1.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.1.7}\leavevmode {\color  {Chapter }IsomorphismMealyGroup}}{73}{subsection.7.1.7}}
\newlabel{IsomorphismMealyGroup}{{7.1.7}{73}{\textcolor {Chapter }{IsomorphismMealyGroup}\relax }{subsection.7.1.7}{}}
\newlabel{IsomorphismMealyMonoid}{{7.1.7}{73}{\textcolor {Chapter }{IsomorphismMealyGroup}\relax }{subsection.7.1.7}{}}
\newlabel{IsomorphismMealySemigroup}{{7.1.7}{73}{\textcolor {Chapter }{IsomorphismMealyGroup}\relax }{subsection.7.1.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.1.8}\leavevmode {\color  {Chapter }FRGroupByVirtualEndomorphism}}{74}{subsection.7.1.8}}
\newlabel{FRGroupByVirtualEndomorphism}{{7.1.8}{74}{\textcolor {Chapter }{FRGroupByVirtualEndomorphism}\relax }{subsection.7.1.8}{}}
\citation{MR2197828}
\citation{MR1995624}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.1.9}\leavevmode {\color  {Chapter }TreeWreathProduct (FR group)}}{75}{subsection.7.1.9}}
\newlabel{TreeWreathProduct:FR group}{{7.1.9}{75}{\textcolor {Chapter }{TreeWreathProduct (FR group)}\relax }{subsection.7.1.9}{}}
\@writefile{brf}{\backcite{MR2197828}{{75}{7.1.9}{subsection.7.1.9}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.1.10}\leavevmode {\color  {Chapter }WeaklyBranchedEmbedding}}{75}{subsection.7.1.10}}
\newlabel{WeaklyBranchedEmbedding}{{7.1.10}{75}{\textcolor {Chapter }{WeaklyBranchedEmbedding}\relax }{subsection.7.1.10}{}}
\@writefile{brf}{\backcite{MR1995624}{{75}{7.1.10}{subsection.7.1.10}}}
\@writefile{toc}{\contentsline {section}{\numberline {7.2}\leavevmode {\color  {Chapter }Operations for FR semigroups}}{75}{section.7.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.1}\leavevmode {\color  {Chapter }PermGroup}}{75}{subsection.7.2.1}}
\newlabel{PermGroup}{{7.2.1}{75}{\textcolor {Chapter }{PermGroup}\relax }{subsection.7.2.1}{}}
\newlabel{EpimorphismPermGroup}{{7.2.1}{75}{\textcolor {Chapter }{PermGroup}\relax }{subsection.7.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.2}\leavevmode {\color  {Chapter }PcGroup}}{76}{subsection.7.2.2}}
\newlabel{PcGroup}{{7.2.2}{76}{\textcolor {Chapter }{PcGroup}\relax }{subsection.7.2.2}{}}
\newlabel{EpimorphismPcGroup}{{7.2.2}{76}{\textcolor {Chapter }{PcGroup}\relax }{subsection.7.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.3}\leavevmode {\color  {Chapter }TransMonoid}}{77}{subsection.7.2.3}}
\newlabel{TransMonoid}{{7.2.3}{77}{\textcolor {Chapter }{TransMonoid}\relax }{subsection.7.2.3}{}}
\newlabel{TransformationMonoid}{{7.2.3}{77}{\textcolor {Chapter }{TransMonoid}\relax }{subsection.7.2.3}{}}
\newlabel{EpimorphismTransMonoid}{{7.2.3}{77}{\textcolor {Chapter }{TransMonoid}\relax }{subsection.7.2.3}{}}
\newlabel{EpimorphismTransformationMonoid}{{7.2.3}{77}{\textcolor {Chapter }{TransMonoid}\relax }{subsection.7.2.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.4}\leavevmode {\color  {Chapter }TransSemigroup}}{77}{subsection.7.2.4}}
\newlabel{TransSemigroup}{{7.2.4}{77}{\textcolor {Chapter }{TransSemigroup}\relax }{subsection.7.2.4}{}}
\newlabel{TransformationSemigroup}{{7.2.4}{77}{\textcolor {Chapter }{TransSemigroup}\relax }{subsection.7.2.4}{}}
\newlabel{EpimorphismTransSemigroup}{{7.2.4}{77}{\textcolor {Chapter }{TransSemigroup}\relax }{subsection.7.2.4}{}}
\newlabel{EpimorphismTransformationSemigroup}{{7.2.4}{77}{\textcolor {Chapter }{TransSemigroup}\relax }{subsection.7.2.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.5}\leavevmode {\color  {Chapter }EpimorphismGermGroup}}{78}{subsection.7.2.5}}
\newlabel{EpimorphismGermGroup}{{7.2.5}{78}{\textcolor {Chapter }{EpimorphismGermGroup}\relax }{subsection.7.2.5}{}}
\newlabel{EpimorphismGermGroup:EGG0}{{7.2.5}{78}{\textcolor {Chapter }{EpimorphismGermGroup}\relax }{subsection.7.2.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.6}\leavevmode {\color  {Chapter }StabilizerImage}}{78}{subsection.7.2.6}}
\newlabel{StabilizerImage}{{7.2.6}{78}{\textcolor {Chapter }{StabilizerImage}\relax }{subsection.7.2.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.7}\leavevmode {\color  {Chapter }LevelStabilizer}}{79}{subsection.7.2.7}}
\newlabel{LevelStabilizer}{{7.2.7}{79}{\textcolor {Chapter }{LevelStabilizer}\relax }{subsection.7.2.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.8}\leavevmode {\color  {Chapter }IsStateClosedFRSemigroup}}{79}{subsection.7.2.8}}
\newlabel{IsStateClosedFRSemigroup}{{7.2.8}{79}{\textcolor {Chapter }{IsStateClosedFRSemigroup}\relax }{subsection.7.2.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.9}\leavevmode {\color  {Chapter }StateClosure}}{80}{subsection.7.2.9}}
\newlabel{StateClosure}{{7.2.9}{80}{\textcolor {Chapter }{StateClosure}\relax }{subsection.7.2.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.10}\leavevmode {\color  {Chapter }IsRecurrentFRSemigroup}}{80}{subsection.7.2.10}}
\newlabel{IsRecurrentFRSemigroup}{{7.2.10}{80}{\textcolor {Chapter }{IsRecurrentFRSemigroup}\relax }{subsection.7.2.10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.11}\leavevmode {\color  {Chapter }IsLevelTransitive (FR group)}}{80}{subsection.7.2.11}}
\newlabel{IsLevelTransitive:FR group}{{7.2.11}{80}{\textcolor {Chapter }{IsLevelTransitive (FR group)}\relax }{subsection.7.2.11}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.12}\leavevmode {\color  {Chapter }IsInfinitelyTransitive}}{81}{subsection.7.2.12}}
\newlabel{IsInfinitelyTransitive}{{7.2.12}{81}{\textcolor {Chapter }{IsInfinitelyTransitive}\relax }{subsection.7.2.12}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.13}\leavevmode {\color  {Chapter }IsFinitaryFRSemigroup}}{81}{subsection.7.2.13}}
\newlabel{IsFinitaryFRSemigroup}{{7.2.13}{81}{\textcolor {Chapter }{IsFinitaryFRSemigroup}\relax }{subsection.7.2.13}{}}
\newlabel{IsWeaklyFinitaryFRSemigroup}{{7.2.13}{81}{\textcolor {Chapter }{IsFinitaryFRSemigroup}\relax }{subsection.7.2.13}{}}
\newlabel{IsBoundedFRSemigroup}{{7.2.13}{81}{\textcolor {Chapter }{IsFinitaryFRSemigroup}\relax }{subsection.7.2.13}{}}
\newlabel{IsPolynomialGrowthFRSemigroup}{{7.2.13}{81}{\textcolor {Chapter }{IsFinitaryFRSemigroup}\relax }{subsection.7.2.13}{}}
\newlabel{IsFiniteStateFRSemigroup}{{7.2.13}{81}{\textcolor {Chapter }{IsFinitaryFRSemigroup}\relax }{subsection.7.2.13}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.14}\leavevmode {\color  {Chapter }Degree (FR semigroup)}}{82}{subsection.7.2.14}}
\newlabel{Degree:FR semigroup}{{7.2.14}{82}{\textcolor {Chapter }{Degree (FR semigroup)}\relax }{subsection.7.2.14}{}}
\newlabel{DegreeOfFRSemigroup}{{7.2.14}{82}{\textcolor {Chapter }{Degree (FR semigroup)}\relax }{subsection.7.2.14}{}}
\newlabel{Depth:FR semigroup}{{7.2.14}{82}{\textcolor {Chapter }{Degree (FR semigroup)}\relax }{subsection.7.2.14}{}}
\newlabel{DepthOfFRSemigroup}{{7.2.14}{82}{\textcolor {Chapter }{Degree (FR semigroup)}\relax }{subsection.7.2.14}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.15}\leavevmode {\color  {Chapter }HasOpenSetConditionFRSemigroup}}{82}{subsection.7.2.15}}
\newlabel{HasOpenSetConditionFRSemigroup}{{7.2.15}{82}{\textcolor {Chapter }{HasOpenSetConditionFRSemigroup}\relax }{subsection.7.2.15}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.16}\leavevmode {\color  {Chapter }IsContracting}}{82}{subsection.7.2.16}}
\newlabel{IsContracting}{{7.2.16}{82}{\textcolor {Chapter }{IsContracting}\relax }{subsection.7.2.16}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.17}\leavevmode {\color  {Chapter }NucleusOfFRSemigroup}}{83}{subsection.7.2.17}}
\newlabel{NucleusOfFRSemigroup}{{7.2.17}{83}{\textcolor {Chapter }{NucleusOfFRSemigroup}\relax }{subsection.7.2.17}{}}
\newlabel{Nucleus:FR semigroup}{{7.2.17}{83}{\textcolor {Chapter }{NucleusOfFRSemigroup}\relax }{subsection.7.2.17}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.18}\leavevmode {\color  {Chapter }NucleusMachine (FR semigroup)}}{83}{subsection.7.2.18}}
\newlabel{NucleusMachine:FR semigroup}{{7.2.18}{83}{\textcolor {Chapter }{NucleusMachine (FR semigroup)}\relax }{subsection.7.2.18}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.19}\leavevmode {\color  {Chapter }AdjacencyBasesWithOne}}{83}{subsection.7.2.19}}
\newlabel{AdjacencyBasesWithOne}{{7.2.19}{83}{\textcolor {Chapter }{AdjacencyBasesWithOne}\relax }{subsection.7.2.19}{}}
\newlabel{AdjacencyPoset}{{7.2.19}{83}{\textcolor {Chapter }{AdjacencyBasesWithOne}\relax }{subsection.7.2.19}{}}
\citation{0810.4936}
\@writefile{brf}{\backcite{0810.4936}{{84}{7.2.19}{subsection.7.2.19}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.20}\leavevmode {\color  {Chapter }BranchingSubgroup}}{84}{subsection.7.2.20}}
\newlabel{BranchingSubgroup}{{7.2.20}{84}{\textcolor {Chapter }{BranchingSubgroup}\relax }{subsection.7.2.20}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.21}\leavevmode {\color  {Chapter }FindBranchingSubgroup}}{85}{subsection.7.2.21}}
\newlabel{FindBranchingSubgroup}{{7.2.21}{85}{\textcolor {Chapter }{FindBranchingSubgroup}\relax }{subsection.7.2.21}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.22}\leavevmode {\color  {Chapter }IsBranched (FR group)}}{85}{subsection.7.2.22}}
\newlabel{IsBranched:FR group}{{7.2.22}{85}{\textcolor {Chapter }{IsBranched (FR group)}\relax }{subsection.7.2.22}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.23}\leavevmode {\color  {Chapter }IsBranchingSubgroup (FR semigroup)}}{85}{subsection.7.2.23}}
\newlabel{IsBranchingSubgroup:FR semigroup}{{7.2.23}{85}{\textcolor {Chapter }{IsBranchingSubgroup (FR semigroup)}\relax }{subsection.7.2.23}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.24}\leavevmode {\color  {Chapter }TopVertexTransformations}}{86}{subsection.7.2.24}}
\newlabel{TopVertexTransformations}{{7.2.24}{86}{\textcolor {Chapter }{TopVertexTransformations}\relax }{subsection.7.2.24}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.25}\leavevmode {\color  {Chapter }VertexTransformations (FR semigroup)}}{86}{subsection.7.2.25}}
\newlabel{VertexTransformations:FR semigroup}{{7.2.25}{86}{\textcolor {Chapter }{VertexTransformations (FR semigroup)}\relax }{subsection.7.2.25}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.26}\leavevmode {\color  {Chapter }VirtualEndomorphism}}{86}{subsection.7.2.26}}
\newlabel{VirtualEndomorphism}{{7.2.26}{86}{\textcolor {Chapter }{VirtualEndomorphism}\relax }{subsection.7.2.26}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.27}\leavevmode {\color  {Chapter }EpimorphismFromFpGroup}}{87}{subsection.7.2.27}}
\newlabel{EpimorphismFromFpGroup}{{7.2.27}{87}{\textcolor {Chapter }{EpimorphismFromFpGroup}\relax }{subsection.7.2.27}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.28}\leavevmode {\color  {Chapter }IsomorphismSubgroupFpGroup}}{87}{subsection.7.2.28}}
\newlabel{IsomorphismSubgroupFpGroup}{{7.2.28}{87}{\textcolor {Chapter }{IsomorphismSubgroupFpGroup}\relax }{subsection.7.2.28}{}}
\newlabel{AsSubgroupFpGroup}{{7.2.28}{87}{\textcolor {Chapter }{IsomorphismSubgroupFpGroup}\relax }{subsection.7.2.28}{}}
\newlabel{IsomorphismLpGroup}{{7.2.28}{87}{\textcolor {Chapter }{IsomorphismSubgroupFpGroup}\relax }{subsection.7.2.28}{}}
\newlabel{AsLpGroup}{{7.2.28}{87}{\textcolor {Chapter }{IsomorphismSubgroupFpGroup}\relax }{subsection.7.2.28}{}}
\citation{MR2009317}
\citation{MR2483125}
\@writefile{brf}{\backcite{MR2009317}{{88}{7.2.28}{subsection.7.2.28}}}
\@writefile{brf}{\backcite{MR2483125}{{88}{7.2.28}{subsection.7.2.28}}}
\@writefile{toc}{\contentsline {section}{\numberline {7.3}\leavevmode {\color  {Chapter }Properties for infinite groups}}{88}{section.7.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.3.1}\leavevmode {\color  {Chapter }IsTorsionGroup}}{88}{subsection.7.3.1}}
\newlabel{IsTorsionGroup}{{7.3.1}{88}{\textcolor {Chapter }{IsTorsionGroup}\relax }{subsection.7.3.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.3.2}\leavevmode {\color  {Chapter }IsTorsionFreeGroup}}{88}{subsection.7.3.2}}
\newlabel{IsTorsionFreeGroup}{{7.3.2}{88}{\textcolor {Chapter }{IsTorsionFreeGroup}\relax }{subsection.7.3.2}{}}
\citation{vneumann}
\citation{MR1839488}
\citation{MR1839489}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.3.3}\leavevmode {\color  {Chapter }IsAmenableGroup}}{89}{subsection.7.3.3}}
\newlabel{IsAmenableGroup}{{7.3.3}{89}{\textcolor {Chapter }{IsAmenableGroup}\relax }{subsection.7.3.3}{}}
\@writefile{brf}{\backcite{vneumann}{{89}{7.3.3}{subsection.7.3.3}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.3.4}\leavevmode {\color  {Chapter }IsVirtuallySimpleGroup}}{89}{subsection.7.3.4}}
\newlabel{IsVirtuallySimpleGroup}{{7.3.4}{89}{\textcolor {Chapter }{IsVirtuallySimpleGroup}\relax }{subsection.7.3.4}{}}
\@writefile{brf}{\backcite{MR1839488}{{89}{7.3.4}{subsection.7.3.4}}}
\@writefile{brf}{\backcite{MR1839489}{{89}{7.3.4}{subsection.7.3.4}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.3.5}\leavevmode {\color  {Chapter }IsResiduallyFinite}}{89}{subsection.7.3.5}}
\newlabel{IsResiduallyFinite}{{7.3.5}{89}{\textcolor {Chapter }{IsResiduallyFinite}\relax }{subsection.7.3.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.3.6}\leavevmode {\color  {Chapter }IsSQUniversal}}{90}{subsection.7.3.6}}
\newlabel{IsSQUniversal}{{7.3.6}{90}{\textcolor {Chapter }{IsSQUniversal}\relax }{subsection.7.3.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.3.7}\leavevmode {\color  {Chapter }IsJustInfinite}}{90}{subsection.7.3.7}}
\newlabel{IsJustInfinite}{{7.3.7}{90}{\textcolor {Chapter }{IsJustInfinite}\relax }{subsection.7.3.7}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {8}\leavevmode {\color  {Chapter }Algebras}}{91}{chapter.8}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{algebras}{{8}{91}{\textcolor {Chapter }{Algebras}\relax }{chapter.8}{}}
\@writefile{toc}{\contentsline {section}{\numberline {8.1}\leavevmode {\color  {Chapter }Creators for FR algebras}}{91}{section.8.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.1}\leavevmode {\color  {Chapter }FRAlgebra}}{91}{subsection.8.1.1}}
\newlabel{FRAlgebra}{{8.1.1}{91}{\textcolor {Chapter }{FRAlgebra}\relax }{subsection.8.1.1}{}}
\newlabel{FRAlgebraWithOne}{{8.1.1}{91}{\textcolor {Chapter }{FRAlgebra}\relax }{subsection.8.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.2}\leavevmode {\color  {Chapter }SCAlgebra}}{92}{subsection.8.1.2}}
\newlabel{SCAlgebra}{{8.1.2}{92}{\textcolor {Chapter }{SCAlgebra}\relax }{subsection.8.1.2}{}}
\newlabel{SCAlgebraWithOne}{{8.1.2}{92}{\textcolor {Chapter }{SCAlgebra}\relax }{subsection.8.1.2}{}}
\newlabel{SCAlgebraNC}{{8.1.2}{92}{\textcolor {Chapter }{SCAlgebra}\relax }{subsection.8.1.2}{}}
\newlabel{SCAlgebraWithOneNC}{{8.1.2}{92}{\textcolor {Chapter }{SCAlgebra}\relax }{subsection.8.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.3}\leavevmode {\color  {Chapter }BranchingIdeal}}{92}{subsection.8.1.3}}
\newlabel{BranchingIdeal}{{8.1.3}{92}{\textcolor {Chapter }{BranchingIdeal}\relax }{subsection.8.1.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {8.2}\leavevmode {\color  {Chapter }Operations for FR algebras}}{92}{section.8.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.2.1}\leavevmode {\color  {Chapter }MatrixQuotient}}{92}{subsection.8.2.1}}
\newlabel{MatrixQuotient}{{8.2.1}{92}{\textcolor {Chapter }{MatrixQuotient}\relax }{subsection.8.2.1}{}}
\newlabel{EpimorphismMatrixQuotient}{{8.2.1}{92}{\textcolor {Chapter }{MatrixQuotient}\relax }{subsection.8.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.2.2}\leavevmode {\color  {Chapter }ThinnedAlgebra}}{93}{subsection.8.2.2}}
\newlabel{ThinnedAlgebra}{{8.2.2}{93}{\textcolor {Chapter }{ThinnedAlgebra}\relax }{subsection.8.2.2}{}}
\newlabel{ThinnedAlgebraWithOne}{{8.2.2}{93}{\textcolor {Chapter }{ThinnedAlgebra}\relax }{subsection.8.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.2.3}\leavevmode {\color  {Chapter }Nillity}}{93}{subsection.8.2.3}}
\newlabel{Nillity}{{8.2.3}{93}{\textcolor {Chapter }{Nillity}\relax }{subsection.8.2.3}{}}
\newlabel{IsNilElement}{{8.2.3}{93}{\textcolor {Chapter }{Nillity}\relax }{subsection.8.2.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.2.4}\leavevmode {\color  {Chapter }DegreeOfHomogeneousElement}}{93}{subsection.8.2.4}}
\newlabel{DegreeOfHomogeneousElement}{{8.2.4}{93}{\textcolor {Chapter }{DegreeOfHomogeneousElement}\relax }{subsection.8.2.4}{}}
\newlabel{IsHomogeneousElement}{{8.2.4}{93}{\textcolor {Chapter }{DegreeOfHomogeneousElement}\relax }{subsection.8.2.4}{}}
\citation{MR2162164}
\@writefile{toc}{\contentsline {chapter}{\numberline {9}\leavevmode {\color  {Chapter }Iterated monodromy groups}}{94}{chapter.9}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{img}{{9}{94}{\textcolor {Chapter }{Iterated monodromy groups}\relax }{chapter.9}{}}
\@writefile{brf}{\backcite{MR2162164}{{94}{9}{chapter.9}}}
\@writefile{toc}{\contentsline {section}{\numberline {9.1}\leavevmode {\color  {Chapter }Creators and operations for IMG machines}}{94}{section.9.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.1}\leavevmode {\color  {Chapter }AsIMGMachine (FR machine)}}{94}{subsection.9.1.1}}
\newlabel{AsIMGMachine:FR machine}{{9.1.1}{94}{\textcolor {Chapter }{AsIMGMachine (FR machine)}\relax }{subsection.9.1.1}{}}
\citation{MR2162164}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.2}\leavevmode {\color  {Chapter }IMGRelator}}{95}{subsection.9.1.2}}
\newlabel{IMGRelator}{{9.1.2}{95}{\textcolor {Chapter }{IMGRelator}\relax }{subsection.9.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.3}\leavevmode {\color  {Chapter }IsKneadingMachine}}{95}{subsection.9.1.3}}
\newlabel{IsKneadingMachine}{{9.1.3}{95}{\textcolor {Chapter }{IsKneadingMachine}\relax }{subsection.9.1.3}{}}
\newlabel{IsPlanarKneadingMachine}{{9.1.3}{95}{\textcolor {Chapter }{IsKneadingMachine}\relax }{subsection.9.1.3}{}}
\@writefile{brf}{\backcite{MR2162164}{{95}{9.1.3}{subsection.9.1.3}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.4}\leavevmode {\color  {Chapter }AsPolynomialFRMachine}}{96}{subsection.9.1.4}}
\newlabel{AsPolynomialFRMachine}{{9.1.4}{96}{\textcolor {Chapter }{AsPolynomialFRMachine}\relax }{subsection.9.1.4}{}}
\newlabel{AsPolynomialIMGMachine}{{9.1.4}{96}{\textcolor {Chapter }{AsPolynomialFRMachine}\relax }{subsection.9.1.4}{}}
\citation{MR762431}
\citation{MR812271}
\citation{MR1149891}
\citation{math.DS/9305207}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.5}\leavevmode {\color  {Chapter }AddingElement (FR machine)}}{97}{subsection.9.1.5}}
\newlabel{AddingElement:FR machine}{{9.1.5}{97}{\textcolor {Chapter }{AddingElement (FR machine)}\relax }{subsection.9.1.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.6}\leavevmode {\color  {Chapter }PolynomialFRMachine}}{97}{subsection.9.1.6}}
\newlabel{PolynomialFRMachine}{{9.1.6}{97}{\textcolor {Chapter }{PolynomialFRMachine}\relax }{subsection.9.1.6}{}}
\newlabel{PolynomialIMGMachine}{{9.1.6}{97}{\textcolor {Chapter }{PolynomialFRMachine}\relax }{subsection.9.1.6}{}}
\newlabel{PolynomialMealyMachine}{{9.1.6}{97}{\textcolor {Chapter }{PolynomialFRMachine}\relax }{subsection.9.1.6}{}}
\@writefile{brf}{\backcite{MR762431}{{97}{9.1.6}{subsection.9.1.6}}}
\@writefile{brf}{\backcite{MR812271}{{97}{9.1.6}{subsection.9.1.6}}}
\@writefile{brf}{\backcite{MR1149891}{{97}{9.1.6}{subsection.9.1.6}}}
\@writefile{brf}{\backcite{math.DS/9305207}{{97}{9.1.6}{subsection.9.1.6}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.7}\leavevmode {\color  {Chapter }ExternalAngles}}{99}{subsection.9.1.7}}
\newlabel{ExternalAngles}{{9.1.7}{99}{\textcolor {Chapter }{ExternalAngles}\relax }{subsection.9.1.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.8}\leavevmode {\color  {Chapter }Lift}}{99}{subsection.9.1.8}}
\newlabel{Lift}{{9.1.8}{99}{\textcolor {Chapter }{Lift}\relax }{subsection.9.1.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.9}\leavevmode {\color  {Chapter }AsGroupFRMachine (endomorphism)}}{100}{subsection.9.1.9}}
\newlabel{AsGroupFRMachine:endomorphism}{{9.1.9}{100}{\textcolor {Chapter }{AsGroupFRMachine (endomorphism)}\relax }{subsection.9.1.9}{}}
\newlabel{AsMonoidFRMachine:endomorphism}{{9.1.9}{100}{\textcolor {Chapter }{AsGroupFRMachine (endomorphism)}\relax }{subsection.9.1.9}{}}
\newlabel{AsSemigroupFRMachine:endomorphism}{{9.1.9}{100}{\textcolor {Chapter }{AsGroupFRMachine (endomorphism)}\relax }{subsection.9.1.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.10}\leavevmode {\color  {Chapter }NormalizedPolynomialFRMachine}}{101}{subsection.9.1.10}}
\newlabel{NormalizedPolynomialFRMachine}{{9.1.10}{101}{\textcolor {Chapter }{NormalizedPolynomialFRMachine}\relax }{subsection.9.1.10}{}}
\newlabel{NormalizedPolynomialIMGMachine}{{9.1.10}{101}{\textcolor {Chapter }{NormalizedPolynomialFRMachine}\relax }{subsection.9.1.10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.11}\leavevmode {\color  {Chapter }Mating}}{101}{subsection.9.1.11}}
\newlabel{Mating}{{9.1.11}{101}{\textcolor {Chapter }{Mating}\relax }{subsection.9.1.11}{}}
\citation{tan:database}
\citation{MR1315537}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.12}\leavevmode {\color  {Chapter }DBRationalIMGGroup}}{102}{subsection.9.1.12}}
\newlabel{DBRationalIMGGroup}{{9.1.12}{102}{\textcolor {Chapter }{DBRationalIMGGroup}\relax }{subsection.9.1.12}{}}
\@writefile{brf}{\backcite{tan:database}{{102}{9.1.12}{subsection.9.1.12}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.13}\leavevmode {\color  {Chapter }PostCriticalMachine}}{102}{subsection.9.1.13}}
\newlabel{PostCriticalMachine}{{9.1.13}{102}{\textcolor {Chapter }{PostCriticalMachine}\relax }{subsection.9.1.13}{}}
\citation{MR1672176}
\@writefile{toc}{\contentsline {section}{\numberline {9.2}\leavevmode {\color  {Chapter }Spiders}}{103}{section.9.2}}
\@writefile{brf}{\backcite{MR1315537}{{103}{9.2}{section.9.2}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.2.1}\leavevmode {\color  {Chapter }DelaunayTriangulation}}{103}{subsection.9.2.1}}
\newlabel{DelaunayTriangulation}{{9.2.1}{103}{\textcolor {Chapter }{DelaunayTriangulation}\relax }{subsection.9.2.1}{}}
\@writefile{brf}{\backcite{MR1672176}{{103}{9.2.1}{subsection.9.2.1}}}
\citation{MR1315537}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.2.2}\leavevmode {\color  {Chapter }LocateInTriangulation}}{104}{subsection.9.2.2}}
\newlabel{LocateInTriangulation}{{9.2.2}{104}{\textcolor {Chapter }{LocateInTriangulation}\relax }{subsection.9.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.2.3}\leavevmode {\color  {Chapter }RationalFunction}}{104}{subsection.9.2.3}}
\newlabel{RationalFunction}{{9.2.3}{104}{\textcolor {Chapter }{RationalFunction}\relax }{subsection.9.2.3}{}}
\@writefile{brf}{\backcite{MR1315537}{{104}{9.2.3}{subsection.9.2.3}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.2.4}\leavevmode {\color  {Chapter }FRMachine (rational function)}}{104}{subsection.9.2.4}}
\newlabel{FRMachine:rational function}{{9.2.4}{104}{\textcolor {Chapter }{FRMachine (rational function)}\relax }{subsection.9.2.4}{}}
\newlabel{IMGMachine:rational function}{{9.2.4}{104}{\textcolor {Chapter }{FRMachine (rational function)}\relax }{subsection.9.2.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.2.5}\leavevmode {\color  {Chapter }FindThurstonObstruction}}{105}{subsection.9.2.5}}
\newlabel{FindThurstonObstruction}{{9.2.5}{105}{\textcolor {Chapter }{FindThurstonObstruction}\relax }{subsection.9.2.5}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {10}\leavevmode {\color  {Chapter }Examples}}{106}{chapter.10}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{frexamples}{{10}{106}{\textcolor {Chapter }{Examples}\relax }{chapter.10}{}}
\@writefile{toc}{\contentsline {section}{\numberline {10.1}\leavevmode {\color  {Chapter }Examples of groups}}{106}{section.10.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.1}\leavevmode {\color  {Chapter }FullBinaryGroup}}{106}{subsection.10.1.1}}
\newlabel{FullBinaryGroup}{{10.1.1}{106}{\textcolor {Chapter }{FullBinaryGroup}\relax }{subsection.10.1.1}{}}
\newlabel{FiniteDepthBinaryGroup}{{10.1.1}{106}{\textcolor {Chapter }{FullBinaryGroup}\relax }{subsection.10.1.1}{}}
\newlabel{FinitaryBinaryGroup}{{10.1.1}{106}{\textcolor {Chapter }{FullBinaryGroup}\relax }{subsection.10.1.1}{}}
\newlabel{BoundedBinaryGroup}{{10.1.1}{106}{\textcolor {Chapter }{FullBinaryGroup}\relax }{subsection.10.1.1}{}}
\newlabel{PolynomialGrowthBinaryGroup}{{10.1.1}{106}{\textcolor {Chapter }{FullBinaryGroup}\relax }{subsection.10.1.1}{}}
\newlabel{FiniteStateBinaryGroup}{{10.1.1}{106}{\textcolor {Chapter }{FullBinaryGroup}\relax }{subsection.10.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.2}\leavevmode {\color  {Chapter }BinaryKneadingGroup}}{106}{subsection.10.1.2}}
\newlabel{BinaryKneadingGroup}{{10.1.2}{106}{\textcolor {Chapter }{BinaryKneadingGroup}\relax }{subsection.10.1.2}{}}
\newlabel{BinaryKneadingMachine}{{10.1.2}{106}{\textcolor {Chapter }{BinaryKneadingGroup}\relax }{subsection.10.1.2}{}}
\citation{MR2176547}
\citation{MR1902367}
\citation{0811.2777}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.3}\leavevmode {\color  {Chapter }BasilicaGroup}}{107}{subsection.10.1.3}}
\newlabel{BasilicaGroup}{{10.1.3}{107}{\textcolor {Chapter }{BasilicaGroup}\relax }{subsection.10.1.3}{}}
\@writefile{brf}{\backcite{MR2176547}{{107}{10.1.3}{subsection.10.1.3}}}
\@writefile{brf}{\backcite{MR1902367}{{107}{10.1.3}{subsection.10.1.3}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.4}\leavevmode {\color  {Chapter }FornaessSibonyGroup}}{107}{subsection.10.1.4}}
\newlabel{FornaessSibonyGroup}{{10.1.4}{107}{\textcolor {Chapter }{FornaessSibonyGroup}\relax }{subsection.10.1.4}{}}
\@writefile{brf}{\backcite{0811.2777}{{107}{10.1.4}{subsection.10.1.4}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.5}\leavevmode {\color  {Chapter }AddingGroup}}{108}{subsection.10.1.5}}
\newlabel{AddingGroup}{{10.1.5}{108}{\textcolor {Chapter }{AddingGroup}\relax }{subsection.10.1.5}{}}
\newlabel{AddingMachine}{{10.1.5}{108}{\textcolor {Chapter }{AddingGroup}\relax }{subsection.10.1.5}{}}
\newlabel{AddingElement}{{10.1.5}{108}{\textcolor {Chapter }{AddingGroup}\relax }{subsection.10.1.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.6}\leavevmode {\color  {Chapter }BinaryAddingGroup}}{108}{subsection.10.1.6}}
\newlabel{BinaryAddingGroup}{{10.1.6}{108}{\textcolor {Chapter }{BinaryAddingGroup}\relax }{subsection.10.1.6}{}}
\newlabel{BinaryAddingMachine}{{10.1.6}{108}{\textcolor {Chapter }{BinaryAddingGroup}\relax }{subsection.10.1.6}{}}
\newlabel{BinaryAddingElement}{{10.1.6}{108}{\textcolor {Chapter }{BinaryAddingGroup}\relax }{subsection.10.1.6}{}}
\citation{MR1856923}
\citation{MR2035113}
\citation{MR2318546}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.7}\leavevmode {\color  {Chapter }MixerGroup}}{109}{subsection.10.1.7}}
\newlabel{MixerGroup}{{10.1.7}{109}{\textcolor {Chapter }{MixerGroup}\relax }{subsection.10.1.7}{}}
\newlabel{MixerMachine}{{10.1.7}{109}{\textcolor {Chapter }{MixerGroup}\relax }{subsection.10.1.7}{}}
\@writefile{brf}{\backcite{MR1856923}{{109}{10.1.7}{subsection.10.1.7}}}
\@writefile{brf}{\backcite{MR2035113}{{109}{10.1.7}{subsection.10.1.7}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.8}\leavevmode {\color  {Chapter }SunicGroup}}{109}{subsection.10.1.8}}
\newlabel{SunicGroup}{{10.1.8}{109}{\textcolor {Chapter }{SunicGroup}\relax }{subsection.10.1.8}{}}
\newlabel{Sunicmachine}{{10.1.8}{109}{\textcolor {Chapter }{SunicGroup}\relax }{subsection.10.1.8}{}}
\@writefile{brf}{\backcite{MR2318546}{{109}{10.1.8}{subsection.10.1.8}}}
\citation{MR764305}
\citation{MR2144977}
\citation{MR565099}
\citation{MR819415}
\citation{MR1899368}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.9}\leavevmode {\color  {Chapter }GrigorchukMachines}}{110}{subsection.10.1.9}}
\newlabel{GrigorchukMachines}{{10.1.9}{110}{\textcolor {Chapter }{GrigorchukMachines}\relax }{subsection.10.1.9}{}}
\newlabel{GrigorchukGroups}{{10.1.9}{110}{\textcolor {Chapter }{GrigorchukMachines}\relax }{subsection.10.1.9}{}}
\@writefile{brf}{\backcite{MR764305}{{110}{10.1.9}{subsection.10.1.9}}}
\@writefile{brf}{\backcite{MR2144977}{{110}{10.1.9}{subsection.10.1.9}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.10}\leavevmode {\color  {Chapter }GrigorchukMachine}}{110}{subsection.10.1.10}}
\newlabel{GrigorchukMachine}{{10.1.10}{110}{\textcolor {Chapter }{GrigorchukMachine}\relax }{subsection.10.1.10}{}}
\newlabel{GrigorchukGroup}{{10.1.10}{110}{\textcolor {Chapter }{GrigorchukMachine}\relax }{subsection.10.1.10}{}}
\@writefile{brf}{\backcite{MR565099}{{110}{10.1.10}{subsection.10.1.10}}}
\@writefile{brf}{\backcite{MR819415}{{110}{10.1.10}{subsection.10.1.10}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.11}\leavevmode {\color  {Chapter }GrigorchukOverGroup}}{110}{subsection.10.1.11}}
\newlabel{GrigorchukOverGroup}{{10.1.11}{110}{\textcolor {Chapter }{GrigorchukOverGroup}\relax }{subsection.10.1.11}{}}
\citation{MR2009317}
\citation{MR1656573}
\@writefile{brf}{\backcite{MR1899368}{{111}{10.1.11}{subsection.10.1.11}}}
\@writefile{brf}{\backcite{MR2009317}{{111}{10.1.11}{subsection.10.1.11}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.12}\leavevmode {\color  {Chapter }GrigorchukTwistedTwin}}{111}{subsection.10.1.12}}
\newlabel{GrigorchukTwistedTwin}{{10.1.12}{111}{\textcolor {Chapter }{GrigorchukTwistedTwin}\relax }{subsection.10.1.12}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.13}\leavevmode {\color  {Chapter }BrunnerSidkiVieiraGroup}}{111}{subsection.10.1.13}}
\newlabel{BrunnerSidkiVieiraGroup}{{10.1.13}{111}{\textcolor {Chapter }{BrunnerSidkiVieiraGroup}\relax }{subsection.10.1.13}{}}
\newlabel{BrunnerSidkiVieiraMachine}{{10.1.13}{111}{\textcolor {Chapter }{BrunnerSidkiVieiraGroup}\relax }{subsection.10.1.13}{}}
\@writefile{brf}{\backcite{MR1656573}{{111}{10.1.13}{subsection.10.1.13}}}
\citation{MR713968}
\citation{MR2318547}
\citation{0604328}
\citation{0610033}
\citation{MR2162164}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.14}\leavevmode {\color  {Chapter }AleshinGroups}}{112}{subsection.10.1.14}}
\newlabel{AleshinGroups}{{10.1.14}{112}{\textcolor {Chapter }{AleshinGroups}\relax }{subsection.10.1.14}{}}
\newlabel{AleshinMachines}{{10.1.14}{112}{\textcolor {Chapter }{AleshinGroups}\relax }{subsection.10.1.14}{}}
\@writefile{brf}{\backcite{MR713968}{{112}{10.1.14}{subsection.10.1.14}}}
\@writefile{brf}{\backcite{MR2318547}{{112}{10.1.14}{subsection.10.1.14}}}
\@writefile{brf}{\backcite{0604328}{{112}{10.1.14}{subsection.10.1.14}}}
\@writefile{brf}{\backcite{0610033}{{112}{10.1.14}{subsection.10.1.14}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.15}\leavevmode {\color  {Chapter }AleshinGroup}}{112}{subsection.10.1.15}}
\newlabel{AleshinGroup}{{10.1.15}{112}{\textcolor {Chapter }{AleshinGroup}\relax }{subsection.10.1.15}{}}
\newlabel{AleshinMachine}{{10.1.15}{112}{\textcolor {Chapter }{AleshinGroup}\relax }{subsection.10.1.15}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.16}\leavevmode {\color  {Chapter }BabyAleshinGroup}}{112}{subsection.10.1.16}}
\newlabel{BabyAleshinGroup}{{10.1.16}{112}{\textcolor {Chapter }{BabyAleshinGroup}\relax }{subsection.10.1.16}{}}
\newlabel{BabyAleshinMachine}{{10.1.16}{112}{\textcolor {Chapter }{BabyAleshinGroup}\relax }{subsection.10.1.16}{}}
\@writefile{brf}{\backcite{MR2162164}{{112}{10.1.16}{subsection.10.1.16}}}
\citation{MR696534}
\citation{MR840129}
\citation{MR1981466}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.17}\leavevmode {\color  {Chapter }SidkiFreeGroup}}{113}{subsection.10.1.17}}
\newlabel{SidkiFreeGroup}{{10.1.17}{113}{\textcolor {Chapter }{SidkiFreeGroup}\relax }{subsection.10.1.17}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.18}\leavevmode {\color  {Chapter }GuptaSidkiGroups}}{113}{subsection.10.1.18}}
\newlabel{GuptaSidkiGroups}{{10.1.18}{113}{\textcolor {Chapter }{GuptaSidkiGroups}\relax }{subsection.10.1.18}{}}
\newlabel{GeneralizedGuptaSidkiGroups}{{10.1.18}{113}{\textcolor {Chapter }{GuptaSidkiGroups}\relax }{subsection.10.1.18}{}}
\newlabel{GuptaSidkiMachines}{{10.1.18}{113}{\textcolor {Chapter }{GuptaSidkiGroups}\relax }{subsection.10.1.18}{}}
\@writefile{brf}{\backcite{MR696534}{{113}{10.1.18}{subsection.10.1.18}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.19}\leavevmode {\color  {Chapter }GuptaSidkiGroup}}{113}{subsection.10.1.19}}
\newlabel{GuptaSidkiGroup}{{10.1.19}{113}{\textcolor {Chapter }{GuptaSidkiGroup}\relax }{subsection.10.1.19}{}}
\newlabel{GuptaSidkiMachine}{{10.1.19}{113}{\textcolor {Chapter }{GuptaSidkiGroup}\relax }{subsection.10.1.19}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.20}\leavevmode {\color  {Chapter }NeumannGroup}}{113}{subsection.10.1.20}}
\newlabel{NeumannGroup}{{10.1.20}{113}{\textcolor {Chapter }{NeumannGroup}\relax }{subsection.10.1.20}{}}
\newlabel{NeumannMachine}{{10.1.20}{113}{\textcolor {Chapter }{NeumannGroup}\relax }{subsection.10.1.20}{}}
\@writefile{brf}{\backcite{MR840129}{{113}{10.1.20}{subsection.10.1.20}}}
\@writefile{brf}{\backcite{MR1981466}{{113}{10.1.20}{subsection.10.1.20}}}
\citation{MR942349}
\citation{MR1153150}
\citation{MR1899368}
\citation{MR1839488}
\citation{MR1839489}
\citation{MR2155175}
\citation{MR713968}
\citation{Rattaggi}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.21}\leavevmode {\color  {Chapter }FabrykowskiGuptaGroup}}{114}{subsection.10.1.21}}
\newlabel{FabrykowskiGuptaGroup}{{10.1.21}{114}{\textcolor {Chapter }{FabrykowskiGuptaGroup}\relax }{subsection.10.1.21}{}}
\newlabel{FabrykowskiGuptaGroups}{{10.1.21}{114}{\textcolor {Chapter }{FabrykowskiGuptaGroup}\relax }{subsection.10.1.21}{}}
\@writefile{brf}{\backcite{MR942349}{{114}{10.1.21}{subsection.10.1.21}}}
\@writefile{brf}{\backcite{MR1153150}{{114}{10.1.21}{subsection.10.1.21}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.22}\leavevmode {\color  {Chapter }ZugadiSpinalGroup}}{114}{subsection.10.1.22}}
\newlabel{ZugadiSpinalGroup}{{10.1.22}{114}{\textcolor {Chapter }{ZugadiSpinalGroup}\relax }{subsection.10.1.22}{}}
\@writefile{brf}{\backcite{MR1899368}{{114}{10.1.22}{subsection.10.1.22}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.23}\leavevmode {\color  {Chapter }GammaPQMachine}}{114}{subsection.10.1.23}}
\newlabel{GammaPQMachine}{{10.1.23}{114}{\textcolor {Chapter }{GammaPQMachine}\relax }{subsection.10.1.23}{}}
\newlabel{GammaPQGroup}{{10.1.23}{114}{\textcolor {Chapter }{GammaPQMachine}\relax }{subsection.10.1.23}{}}
\@writefile{brf}{\backcite{MR1839488}{{114}{10.1.23}{subsection.10.1.23}}}
\@writefile{brf}{\backcite{MR1839489}{{114}{10.1.23}{subsection.10.1.23}}}
\@writefile{brf}{\backcite{MR2155175}{{114}{10.1.23}{subsection.10.1.23}}}
\@writefile{brf}{\backcite{MR713968}{{114}{10.1.23}{subsection.10.1.23}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.24}\leavevmode {\color  {Chapter }RattaggiGroup}}{114}{subsection.10.1.24}}
\newlabel{RattaggiGroup}{{10.1.24}{114}{\textcolor {Chapter }{RattaggiGroup}\relax }{subsection.10.1.24}{}}
\@writefile{brf}{\backcite{Rattaggi}{{114}{10.1.24}{subsection.10.1.24}}}
\citation{MR2217913}
\citation{MR2140091}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.25}\leavevmode {\color  {Chapter }HanoiGroup}}{115}{subsection.10.1.25}}
\newlabel{HanoiGroup}{{10.1.25}{115}{\textcolor {Chapter }{HanoiGroup}\relax }{subsection.10.1.25}{}}
\@writefile{brf}{\backcite{MR2217913}{{115}{10.1.25}{subsection.10.1.25}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.26}\leavevmode {\color  {Chapter }DahmaniGroup}}{115}{subsection.10.1.26}}
\newlabel{DahmaniGroup}{{10.1.26}{115}{\textcolor {Chapter }{DahmaniGroup}\relax }{subsection.10.1.26}{}}
\@writefile{brf}{\backcite{MR2140091}{{115}{10.1.26}{subsection.10.1.26}}}
\citation{MR2139928}
\citation{MR0142635}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.27}\leavevmode {\color  {Chapter }MamaghaniGroup}}{116}{subsection.10.1.27}}
\newlabel{MamaghaniGroup}{{10.1.27}{116}{\textcolor {Chapter }{MamaghaniGroup}\relax }{subsection.10.1.27}{}}
\@writefile{brf}{\backcite{MR2139928}{{116}{10.1.27}{subsection.10.1.27}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.28}\leavevmode {\color  {Chapter }WeierstrassGroup}}{116}{subsection.10.1.28}}
\newlabel{WeierstrassGroup}{{10.1.28}{116}{\textcolor {Chapter }{WeierstrassGroup}\relax }{subsection.10.1.28}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.29}\leavevmode {\color  {Chapter }FRAffineGroup}}{116}{subsection.10.1.29}}
\newlabel{FRAffineGroup}{{10.1.29}{116}{\textcolor {Chapter }{FRAffineGroup}\relax }{subsection.10.1.29}{}}
\@writefile{brf}{\backcite{MR0142635}{{116}{10.1.29}{subsection.10.1.29}}}
\citation{MR2197829}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.1.30}\leavevmode {\color  {Chapter }CayleyGroup}}{117}{subsection.10.1.30}}
\newlabel{CayleyGroup}{{10.1.30}{117}{\textcolor {Chapter }{CayleyGroup}\relax }{subsection.10.1.30}{}}
\newlabel{CayleyMachine}{{10.1.30}{117}{\textcolor {Chapter }{CayleyGroup}\relax }{subsection.10.1.30}{}}
\newlabel{LamplighterGroup}{{10.1.30}{117}{\textcolor {Chapter }{CayleyGroup}\relax }{subsection.10.1.30}{}}
\@writefile{brf}{\backcite{MR2197829}{{117}{10.1.30}{subsection.10.1.30}}}
\citation{MR2194959}
\citation{MR2394721}
\citation{MR2293788}
\citation{MR2390328}
\@writefile{toc}{\contentsline {section}{\numberline {10.2}\leavevmode {\color  {Chapter }Examples of semigroups}}{118}{section.10.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.2.1}\leavevmode {\color  {Chapter }I2Machine}}{118}{subsection.10.2.1}}
\newlabel{I2Machine}{{10.2.1}{118}{\textcolor {Chapter }{I2Machine}\relax }{subsection.10.2.1}{}}
\newlabel{I2Monoid}{{10.2.1}{118}{\textcolor {Chapter }{I2Machine}\relax }{subsection.10.2.1}{}}
\@writefile{brf}{\backcite{MR2194959}{{118}{10.2.1}{subsection.10.2.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.2.2}\leavevmode {\color  {Chapter }I4Machine}}{118}{subsection.10.2.2}}
\newlabel{I4Machine}{{10.2.2}{118}{\textcolor {Chapter }{I4Machine}\relax }{subsection.10.2.2}{}}
\newlabel{I4Monoid}{{10.2.2}{118}{\textcolor {Chapter }{I4Machine}\relax }{subsection.10.2.2}{}}
\@writefile{brf}{\backcite{MR2394721}{{118}{10.2.2}{subsection.10.2.2}}}
\@writefile{toc}{\contentsline {section}{\numberline {10.3}\leavevmode {\color  {Chapter }Examples of algebras}}{118}{section.10.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.3.1}\leavevmode {\color  {Chapter }PSZAlgebra}}{118}{subsection.10.3.1}}
\newlabel{PSZAlgebra}{{10.3.1}{118}{\textcolor {Chapter }{PSZAlgebra}\relax }{subsection.10.3.1}{}}
\citation{PSZ}
\citation{MR2254535}
\citation{MR1423285}
\@writefile{brf}{\backcite{MR2293788}{{119}{10.3.1}{subsection.10.3.1}}}
\@writefile{brf}{\backcite{MR2390328}{{119}{10.3.1}{subsection.10.3.1}}}
\@writefile{brf}{\backcite{PSZ}{{119}{10.3.1}{subsection.10.3.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.3.2}\leavevmode {\color  {Chapter }GrigorchukThinnedAlgebra}}{119}{subsection.10.3.2}}
\newlabel{GrigorchukThinnedAlgebra}{{10.3.2}{119}{\textcolor {Chapter }{GrigorchukThinnedAlgebra}\relax }{subsection.10.3.2}{}}
\@writefile{brf}{\backcite{MR2254535}{{119}{10.3.2}{subsection.10.3.2}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.3.3}\leavevmode {\color  {Chapter }GuptaSidkiThinnedAlgebra}}{119}{subsection.10.3.3}}
\newlabel{GuptaSidkiThinnedAlgebra}{{10.3.3}{119}{\textcolor {Chapter }{GuptaSidkiThinnedAlgebra}\relax }{subsection.10.3.3}{}}
\@writefile{brf}{\backcite{MR1423285}{{119}{10.3.3}{subsection.10.3.3}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.3.4}\leavevmode {\color  {Chapter }GrigorchukLieAlgebra}}{120}{subsection.10.3.4}}
\newlabel{GrigorchukLieAlgebra}{{10.3.4}{120}{\textcolor {Chapter }{GrigorchukLieAlgebra}\relax }{subsection.10.3.4}{}}
\newlabel{GuptaSidkiLieAlgebra}{{10.3.4}{120}{\textcolor {Chapter }{GrigorchukLieAlgebra}\relax }{subsection.10.3.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.3.5}\leavevmode {\color  {Chapter }SidkiFreeAlgebra}}{120}{subsection.10.3.5}}
\newlabel{SidkiFreeAlgebra}{{10.3.5}{120}{\textcolor {Chapter }{SidkiFreeAlgebra}\relax }{subsection.10.3.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.3.6}\leavevmode {\color  {Chapter }SidkiMonomialAlgebra}}{120}{subsection.10.3.6}}
\newlabel{SidkiMonomialAlgebra}{{10.3.6}{120}{\textcolor {Chapter }{SidkiMonomialAlgebra}\relax }{subsection.10.3.6}{}}
\citation{MR2422072}
\@writefile{toc}{\contentsline {section}{\numberline {10.4}\leavevmode {\color  {Chapter }Bacher's determinant identities}}{121}{section.10.4}}
\newlabel{bacher}{{10.4}{121}{\textcolor {Chapter }{Bacher's determinant identities}\relax }{section.10.4}{}}
\@writefile{brf}{\backcite{MR2422072}{{121}{10.4}{section.10.4}}}
\citation{MR1839488}
\citation{MR1839489}
\@writefile{toc}{\contentsline {section}{\numberline {10.5}\leavevmode {\color  {Chapter }VH groups}}{124}{section.10.5}}
\newlabel{vhgroups}{{10.5}{124}{\textcolor {Chapter }{VH groups}\relax }{section.10.5}{}}
\@writefile{brf}{\backcite{MR1839488}{{124}{10.5}{section.10.5}}}
\@writefile{brf}{\backcite{MR1839489}{{124}{10.5}{section.10.5}}}
\citation{Rattaggi}
\@writefile{brf}{\backcite{Rattaggi}{{125}{10.5}{section.10.5}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.5.1}\leavevmode {\color  {Chapter }VHStructure}}{125}{subsection.10.5.1}}
\newlabel{VHStructure}{{10.5.1}{125}{\textcolor {Chapter }{VHStructure}\relax }{subsection.10.5.1}{}}
\newlabel{IsVHGroup}{{10.5.1}{125}{\textcolor {Chapter }{VHStructure}\relax }{subsection.10.5.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.5.2}\leavevmode {\color  {Chapter }VerticalAction}}{125}{subsection.10.5.2}}
\newlabel{VerticalAction}{{10.5.2}{125}{\textcolor {Chapter }{VerticalAction}\relax }{subsection.10.5.2}{}}
\newlabel{HorizontalAction}{{10.5.2}{125}{\textcolor {Chapter }{VerticalAction}\relax }{subsection.10.5.2}{}}
\citation{MR1446574}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.5.3}\leavevmode {\color  {Chapter }VHGroup}}{126}{subsection.10.5.3}}
\newlabel{VHGroup}{{10.5.3}{126}{\textcolor {Chapter }{VHGroup}\relax }{subsection.10.5.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.5.4}\leavevmode {\color  {Chapter }IsIrreducibleVHGroup}}{126}{subsection.10.5.4}}
\newlabel{IsIrreducibleVHGroup}{{10.5.4}{126}{\textcolor {Chapter }{IsIrreducibleVHGroup}\relax }{subsection.10.5.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.5.5}\leavevmode {\color  {Chapter }MaximalSimpleSubgroup}}{126}{subsection.10.5.5}}
\newlabel{MaximalSimpleSubgroup}{{10.5.5}{126}{\textcolor {Chapter }{MaximalSimpleSubgroup}\relax }{subsection.10.5.5}{}}
\@writefile{brf}{\backcite{MR1446574}{{127}{10.5.5}{subsection.10.5.5}}}
\@writefile{toc}{\contentsline {chapter}{\numberline {11}\leavevmode {\color  {Chapter }FR implementation details}}{128}{chapter.11}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {11.1}\leavevmode {\color  {Chapter }The family of FR objects}}{128}{section.11.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.1.1}\leavevmode {\color  {Chapter }FRMFamily}}{128}{subsection.11.1.1}}
\newlabel{FRMFamily}{{11.1.1}{128}{\textcolor {Chapter }{FRMFamily}\relax }{subsection.11.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.1.2}\leavevmode {\color  {Chapter }FREFamily}}{128}{subsection.11.1.2}}
\newlabel{FREFamily}{{11.1.2}{128}{\textcolor {Chapter }{FREFamily}\relax }{subsection.11.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.1.3}\leavevmode {\color  {Chapter }AlphabetOfFRObject}}{128}{subsection.11.1.3}}
\newlabel{AlphabetOfFRObject}{{11.1.3}{128}{\textcolor {Chapter }{AlphabetOfFRObject}\relax }{subsection.11.1.3}{}}
\newlabel{AlphabetOfFRAlgebra}{{11.1.3}{128}{\textcolor {Chapter }{AlphabetOfFRObject}\relax }{subsection.11.1.3}{}}
\newlabel{AlphabetOfFRSemigroup}{{11.1.3}{128}{\textcolor {Chapter }{AlphabetOfFRObject}\relax }{subsection.11.1.3}{}}
\newlabel{Alphabet}{{11.1.3}{128}{\textcolor {Chapter }{AlphabetOfFRObject}\relax }{subsection.11.1.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.1.4}\leavevmode {\color  {Chapter }AsPermutation (FR object)}}{129}{subsection.11.1.4}}
\newlabel{AsPermutation:FR object}{{11.1.4}{129}{\textcolor {Chapter }{AsPermutation (FR object)}\relax }{subsection.11.1.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.1.5}\leavevmode {\color  {Chapter }AsTransformation (FR object)}}{129}{subsection.11.1.5}}
\newlabel{AsTransformation:FR object}{{11.1.5}{129}{\textcolor {Chapter }{AsTransformation (FR object)}\relax }{subsection.11.1.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {11.2}\leavevmode {\color  {Chapter }Filters for \texttt  {FRObject}s}}{129}{section.11.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.1}\leavevmode {\color  {Chapter }IsGroupFRMachine}}{129}{subsection.11.2.1}}
\newlabel{IsGroupFRMachine}{{11.2.1}{129}{\textcolor {Chapter }{IsGroupFRMachine}\relax }{subsection.11.2.1}{}}
\newlabel{IsMonoidFRMachine}{{11.2.1}{129}{\textcolor {Chapter }{IsGroupFRMachine}\relax }{subsection.11.2.1}{}}
\newlabel{IsSemigroupFRMachine}{{11.2.1}{129}{\textcolor {Chapter }{IsGroupFRMachine}\relax }{subsection.11.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.2}\leavevmode {\color  {Chapter }IsFRMachineStrRep}}{129}{subsection.11.2.2}}
\newlabel{IsFRMachineStrRep}{{11.2.2}{129}{\textcolor {Chapter }{IsFRMachineStrRep}\relax }{subsection.11.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.3}\leavevmode {\color  {Chapter }IsMealyMachine}}{129}{subsection.11.2.3}}
\newlabel{IsMealyMachine}{{11.2.3}{129}{\textcolor {Chapter }{IsMealyMachine}\relax }{subsection.11.2.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.4}\leavevmode {\color  {Chapter }IsMealyElement}}{130}{subsection.11.2.4}}
\newlabel{IsMealyElement}{{11.2.4}{130}{\textcolor {Chapter }{IsMealyElement}\relax }{subsection.11.2.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.5}\leavevmode {\color  {Chapter }IsMealyMachineIntRep}}{130}{subsection.11.2.5}}
\newlabel{IsMealyMachineIntRep}{{11.2.5}{130}{\textcolor {Chapter }{IsMealyMachineIntRep}\relax }{subsection.11.2.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.6}\leavevmode {\color  {Chapter }IsMealyMachineDomainRep}}{130}{subsection.11.2.6}}
\newlabel{IsMealyMachineDomainRep}{{11.2.6}{130}{\textcolor {Chapter }{IsMealyMachineDomainRep}\relax }{subsection.11.2.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.7}\leavevmode {\color  {Chapter }IsVectorFRMachineRep}}{130}{subsection.11.2.7}}
\newlabel{IsVectorFRMachineRep}{{11.2.7}{130}{\textcolor {Chapter }{IsVectorFRMachineRep}\relax }{subsection.11.2.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.8}\leavevmode {\color  {Chapter }IsAlgebraFRMachineRep}}{130}{subsection.11.2.8}}
\newlabel{IsAlgebraFRMachineRep}{{11.2.8}{130}{\textcolor {Chapter }{IsAlgebraFRMachineRep}\relax }{subsection.11.2.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.9}\leavevmode {\color  {Chapter }IsLinearFRMachine}}{130}{subsection.11.2.9}}
\newlabel{IsLinearFRMachine}{{11.2.9}{130}{\textcolor {Chapter }{IsLinearFRMachine}\relax }{subsection.11.2.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.10}\leavevmode {\color  {Chapter }IsLinearFRElement}}{131}{subsection.11.2.10}}
\newlabel{IsLinearFRElement}{{11.2.10}{131}{\textcolor {Chapter }{IsLinearFRElement}\relax }{subsection.11.2.10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.11}\leavevmode {\color  {Chapter }IsFRElement}}{131}{subsection.11.2.11}}
\newlabel{IsFRElement}{{11.2.11}{131}{\textcolor {Chapter }{IsFRElement}\relax }{subsection.11.2.11}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.12}\leavevmode {\color  {Chapter }IsFRObject}}{131}{subsection.11.2.12}}
\newlabel{IsFRObject}{{11.2.12}{131}{\textcolor {Chapter }{IsFRObject}\relax }{subsection.11.2.12}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.13}\leavevmode {\color  {Chapter }IsFRMachine}}{131}{subsection.11.2.13}}
\newlabel{IsFRMachine}{{11.2.13}{131}{\textcolor {Chapter }{IsFRMachine}\relax }{subsection.11.2.13}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.14}\leavevmode {\color  {Chapter }IsInvertible}}{131}{subsection.11.2.14}}
\newlabel{IsInvertible}{{11.2.14}{131}{\textcolor {Chapter }{IsInvertible}\relax }{subsection.11.2.14}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.15}\leavevmode {\color  {Chapter }IsFRGroup}}{132}{subsection.11.2.15}}
\newlabel{IsFRGroup}{{11.2.15}{132}{\textcolor {Chapter }{IsFRGroup}\relax }{subsection.11.2.15}{}}
\newlabel{IsFRMonoid}{{11.2.15}{132}{\textcolor {Chapter }{IsFRGroup}\relax }{subsection.11.2.15}{}}
\newlabel{IsFRSemigroup}{{11.2.15}{132}{\textcolor {Chapter }{IsFRGroup}\relax }{subsection.11.2.15}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.16}\leavevmode {\color  {Chapter }IsFRAlgebra}}{132}{subsection.11.2.16}}
\newlabel{IsFRAlgebra}{{11.2.16}{132}{\textcolor {Chapter }{IsFRAlgebra}\relax }{subsection.11.2.16}{}}
\newlabel{IsFRAlgebraWithOne}{{11.2.16}{132}{\textcolor {Chapter }{IsFRAlgebra}\relax }{subsection.11.2.16}{}}
\@writefile{toc}{\contentsline {section}{\numberline {11.3}\leavevmode {\color  {Chapter }Some of the algorithms implemented}}{132}{section.11.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.3.1}\leavevmode {\color  {Chapter }FRMachineRWS}}{132}{subsection.11.3.1}}
\newlabel{FRMachineRWS}{{11.3.1}{132}{\textcolor {Chapter }{FRMachineRWS}\relax }{subsection.11.3.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.3.2}\leavevmode {\color  {Chapter }Order of FR elements}}{132}{subsection.11.3.2}}
\citation{MR1839488}
\citation{MR2009317}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.3.3}\leavevmode {\color  {Chapter }Membership in semigroups}}{133}{subsection.11.3.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.3.4}\leavevmode {\color  {Chapter }Order of groups}}{133}{subsection.11.3.4}}
\@writefile{brf}{\backcite{MR1839488}{{133}{11.3.4}{subsection.11.3.4}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.3.5}\leavevmode {\color  {Chapter }Images and preimages of some groups in f.p. and l.p. groups}}{133}{subsection.11.3.5}}
\newlabel{preimages}{{11.3.5}{133}{\textcolor {Chapter }{Images and preimages of some groups in f.p. and l.p. groups}\relax }{subsection.11.3.5}{}}
\@writefile{brf}{\backcite{MR2009317}{{133}{11.3.5}{subsection.11.3.5}}}
\citation{MR2422072}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.3.6}\leavevmode {\color  {Chapter }Comparison of FR, Mealy, vector, and algebra elements}}{134}{subsection.11.3.6}}
\newlabel{sorting}{{11.3.6}{134}{\textcolor {Chapter }{Comparison of FR, Mealy, vector, and algebra elements}\relax }{subsection.11.3.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.3.7}\leavevmode {\color  {Chapter }Inverses of linear elements}}{134}{subsection.11.3.7}}
\@writefile{brf}{\backcite{MR2422072}{{134}{11.3.7}{subsection.11.3.7}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.3.8}\leavevmode {\color  {Chapter }Spiders}}{135}{subsection.11.3.8}}
\@writefile{toc}{\contentsline {chapter}{\numberline {12}\leavevmode {\color  {Chapter }Miscellanea}}{137}{chapter.12}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {12.1}\leavevmode {\color  {Chapter }Helpers}}{137}{section.12.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.1}\leavevmode {\color  {Chapter }TensorSum}}{137}{subsection.12.1.1}}
\newlabel{TensorSum}{{12.1.1}{137}{\textcolor {Chapter }{TensorSum}\relax }{subsection.12.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.2}\leavevmode {\color  {Chapter }TensorProduct}}{137}{subsection.12.1.2}}
\newlabel{TensorProduct}{{12.1.2}{137}{\textcolor {Chapter }{TensorProduct}\relax }{subsection.12.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.3}\leavevmode {\color  {Chapter }DirectSum}}{137}{subsection.12.1.3}}
\newlabel{DirectSum}{{12.1.3}{137}{\textcolor {Chapter }{DirectSum}\relax }{subsection.12.1.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.4}\leavevmode {\color  {Chapter }PeriodicList}}{137}{subsection.12.1.4}}
\newlabel{PeriodicList}{{12.1.4}{137}{\textcolor {Chapter }{PeriodicList}\relax }{subsection.12.1.4}{}}
\newlabel{PeriodicList:period, looping point}{{12.1.4}{137}{\textcolor {Chapter }{PeriodicList}\relax }{subsection.12.1.4}{}}
\newlabel{PeriodicList:list, function}{{12.1.4}{137}{\textcolor {Chapter }{PeriodicList}\relax }{subsection.12.1.4}{}}
\newlabel{CompressedPeriodicList}{{12.1.4}{137}{\textcolor {Chapter }{PeriodicList}\relax }{subsection.12.1.4}{}}
\newlabel{CompressedPeriodicList:period, looping point}{{12.1.4}{137}{\textcolor {Chapter }{PeriodicList}\relax }{subsection.12.1.4}{}}
\newlabel{PrePeriod}{{12.1.4}{137}{\textcolor {Chapter }{PeriodicList}\relax }{subsection.12.1.4}{}}
\newlabel{Period}{{12.1.4}{137}{\textcolor {Chapter }{PeriodicList}\relax }{subsection.12.1.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.5}\leavevmode {\color  {Chapter }CompressPeriodicList}}{138}{subsection.12.1.5}}
\newlabel{CompressPeriodicList}{{12.1.5}{138}{\textcolor {Chapter }{CompressPeriodicList}\relax }{subsection.12.1.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.6}\leavevmode {\color  {Chapter }IsConfinal}}{138}{subsection.12.1.6}}
\newlabel{IsConfinal}{{12.1.6}{138}{\textcolor {Chapter }{IsConfinal}\relax }{subsection.12.1.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.7}\leavevmode {\color  {Chapter }ConfinalityClass}}{139}{subsection.12.1.7}}
\newlabel{ConfinalityClass}{{12.1.7}{139}{\textcolor {Chapter }{ConfinalityClass}\relax }{subsection.12.1.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.8}\leavevmode {\color  {Chapter }LargestCommonPrefix}}{139}{subsection.12.1.8}}
\newlabel{LargestCommonPrefix}{{12.1.8}{139}{\textcolor {Chapter }{LargestCommonPrefix}\relax }{subsection.12.1.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.9}\leavevmode {\color  {Chapter }WordGrowth}}{139}{subsection.12.1.9}}
\newlabel{WordGrowth}{{12.1.9}{139}{\textcolor {Chapter }{WordGrowth}\relax }{subsection.12.1.9}{}}
\newlabel{WordGrowth:1arg}{{12.1.9}{139}{\textcolor {Chapter }{WordGrowth}\relax }{subsection.12.1.9}{}}
\newlabel{OrbitGrowth}{{12.1.9}{139}{\textcolor {Chapter }{WordGrowth}\relax }{subsection.12.1.9}{}}
\newlabel{Ball}{{12.1.9}{139}{\textcolor {Chapter }{WordGrowth}\relax }{subsection.12.1.9}{}}
\newlabel{Sphere}{{12.1.9}{139}{\textcolor {Chapter }{WordGrowth}\relax }{subsection.12.1.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.10}\leavevmode {\color  {Chapter }ShortGroupRelations}}{141}{subsection.12.1.10}}
\newlabel{ShortGroupRelations}{{12.1.10}{141}{\textcolor {Chapter }{ShortGroupRelations}\relax }{subsection.12.1.10}{}}
\newlabel{ShortMonoidRelations}{{12.1.10}{141}{\textcolor {Chapter }{ShortGroupRelations}\relax }{subsection.12.1.10}{}}
\citation{MR2043362}
\citation{MR1314589}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.11}\leavevmode {\color  {Chapter }ShortGroupWordInSet}}{142}{subsection.12.1.11}}
\newlabel{ShortGroupWordInSet}{{12.1.11}{142}{\textcolor {Chapter }{ShortGroupWordInSet}\relax }{subsection.12.1.11}{}}
\newlabel{ShortMonoidWordInSet}{{12.1.11}{142}{\textcolor {Chapter }{ShortGroupWordInSet}\relax }{subsection.12.1.11}{}}
\newlabel{ShortSemigroupWordInSet}{{12.1.11}{142}{\textcolor {Chapter }{ShortGroupWordInSet}\relax }{subsection.12.1.11}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.12}\leavevmode {\color  {Chapter }SurfaceBraidFpGroup}}{142}{subsection.12.1.12}}
\newlabel{SurfaceBraidFpGroup}{{12.1.12}{142}{\textcolor {Chapter }{SurfaceBraidFpGroup}\relax }{subsection.12.1.12}{}}
\newlabel{PureSurfaceBraidFpGroup}{{12.1.12}{142}{\textcolor {Chapter }{SurfaceBraidFpGroup}\relax }{subsection.12.1.12}{}}
\@writefile{brf}{\backcite{MR2043362}{{142}{12.1.12}{subsection.12.1.12}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.13}\leavevmode {\color  {Chapter }CharneyBraidFpGroup}}{142}{subsection.12.1.13}}
\newlabel{CharneyBraidFpGroup}{{12.1.13}{142}{\textcolor {Chapter }{CharneyBraidFpGroup}\relax }{subsection.12.1.13}{}}
\@writefile{brf}{\backcite{MR1314589}{{143}{12.1.13}{subsection.12.1.13}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.14}\leavevmode {\color  {Chapter }ArtinRepresentation}}{143}{subsection.12.1.14}}
\newlabel{ArtinRepresentation}{{12.1.14}{143}{\textcolor {Chapter }{ArtinRepresentation}\relax }{subsection.12.1.14}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.15}\leavevmode {\color  {Chapter }StringByInt}}{143}{subsection.12.1.15}}
\newlabel{StringByInt}{{12.1.15}{143}{\textcolor {Chapter }{StringByInt}\relax }{subsection.12.1.15}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.16}\leavevmode {\color  {Chapter }PositionInTower}}{143}{subsection.12.1.16}}
\newlabel{PositionInTower}{{12.1.16}{143}{\textcolor {Chapter }{PositionInTower}\relax }{subsection.12.1.16}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.17}\leavevmode {\color  {Chapter }RenameSubobjects}}{143}{subsection.12.1.17}}
\newlabel{RenameSubobjects}{{12.1.17}{143}{\textcolor {Chapter }{RenameSubobjects}\relax }{subsection.12.1.17}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.18}\leavevmode {\color  {Chapter }CoefficientsInAbelianExtension}}{143}{subsection.12.1.18}}
\newlabel{CoefficientsInAbelianExtension}{{12.1.18}{143}{\textcolor {Chapter }{CoefficientsInAbelianExtension}\relax }{subsection.12.1.18}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.19}\leavevmode {\color  {Chapter }MagmaEndomorphismByImagesNC}}{144}{subsection.12.1.19}}
\newlabel{MagmaEndomorphismByImagesNC}{{12.1.19}{144}{\textcolor {Chapter }{MagmaEndomorphismByImagesNC}\relax }{subsection.12.1.19}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.20}\leavevmode {\color  {Chapter }MagmaHomomorphismByImagesNC}}{144}{subsection.12.1.20}}
\newlabel{MagmaHomomorphismByImagesNC}{{12.1.20}{144}{\textcolor {Chapter }{MagmaHomomorphismByImagesNC}\relax }{subsection.12.1.20}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.21}\leavevmode {\color  {Chapter }NewFIFO}}{144}{subsection.12.1.21}}
\newlabel{NewFIFO}{{12.1.21}{144}{\textcolor {Chapter }{NewFIFO}\relax }{subsection.12.1.21}{}}
\newlabel{Add:FIFO}{{12.1.21}{144}{\textcolor {Chapter }{NewFIFO}\relax }{subsection.12.1.21}{}}
\newlabel{Append:FIFO}{{12.1.21}{144}{\textcolor {Chapter }{NewFIFO}\relax }{subsection.12.1.21}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.22}\leavevmode {\color  {Chapter }ProductIdeal}}{144}{subsection.12.1.22}}
\newlabel{ProductIdeal}{{12.1.22}{144}{\textcolor {Chapter }{ProductIdeal}\relax }{subsection.12.1.22}{}}
\newlabel{ProductBOIIdeal}{{12.1.22}{144}{\textcolor {Chapter }{ProductIdeal}\relax }{subsection.12.1.22}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.23}\leavevmode {\color  {Chapter }DimensionSeries}}{145}{subsection.12.1.23}}
\newlabel{DimensionSeries}{{12.1.23}{145}{\textcolor {Chapter }{DimensionSeries}\relax }{subsection.12.1.23}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.1.24}\leavevmode {\color  {Chapter }Trans}}{145}{subsection.12.1.24}}
\newlabel{Trans}{{12.1.24}{145}{\textcolor {Chapter }{Trans}\relax }{subsection.12.1.24}{}}
\bibstyle{alpha}
\bibdata{frbib.xml}
\@writefile{toc}{\contentsline {section}{\numberline {12.2}\leavevmode {\color  {Chapter }User settings}}{146}{section.12.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.2.1}\leavevmode {\color  {Chapter }InfoFR}}{146}{subsection.12.2.1}}
\newlabel{InfoFR}{{12.2.1}{146}{\textcolor {Chapter }{InfoFR}\relax }{subsection.12.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {12.2.2}\leavevmode {\color  {Chapter }SEARCH@}}{146}{subsection.12.2.2}}
\newlabel{SEARCH@}{{12.2.2}{146}{\textcolor {Chapter }{SEARCH@}\relax }{subsection.12.2.2}{}}
\bibcite{MR713968}{Ale83}
\bibcite{MR2422072}{Bac08}
\bibcite{MR2009317}{Bar03a}
\bibcite{MR1981466}{Bar03b}
\bibcite{MR2254535}{Bar06}
\bibcite{MR2483125}{BEH08}
\bibcite{MR2043362}{Bel04}
\bibcite{MR1149891}{BFH92}
\bibcite{MR1899368}{BG02}
\bibcite{MR2091700}{BGN03}
\bibcite{MR2035113}{BG{\v S}03}
\bibcite{MR1446574}{BM97}
\bibcite{MR1839488}{BM00a}
\bibcite{MR1839489}{BM00b}
\bibcite{MR2394721}{BR08}
\bibcite{MR2194959}{BRS06}
\bibcite{MR0142635}{BS62}
\bibcite{MR1856923}{B{\v S}01}
\bibcite{MR1656573}{BSV99}
\bibcite{MR2176547}{BV05}
\bibcite{MR1314589}{Cha95}
\bibcite{MR2140091}{Dah05}
\bibcite{MR762431}{DH84}
\bibcite{MR812271}{DH85}
\bibcite{MR2144977}{Ers04}
\bibcite{MR942349}{FG85}
\bibcite{MR1153150}{FG91}
\bibcite{MR2155175}{GM05}
\bibcite{MR565099}{Gri80}
\bibcite{MR764305}{Gri84}
\bibcite{MR696534}{GS83}
\bibcite{MR2217913}{G{\v S}06}
\bibcite{MR1902367}{G{\.Z}02}
\bibcite{MR1315537}{HS94}
\bibcite{MR819415}{Lys85}
\bibcite{MR2139928}{Mam03}
\bibcite{MR1841119}{MNS00}
\bibcite{MR2162164}{Nek05}
\bibcite{0810.4936}{Nek08a}
\bibcite{0811.2777}{Nek08b}
\bibcite{MR840129}{Neu86}
\bibcite{MR2293788}{Pet06}
\bibcite{math.DS/9305207}{Poi}
\bibcite{PSZ}{PSZ}
\bibcite{Rattaggi}{Rat04}
\bibcite{MR1672176}{Ren97}
\bibcite{MR1423285}{Sid97}
\bibcite{MR1774362}{Sid00}
\bibcite{MR2197828}{Sid05}
\bibcite{MR2197829}{SS05}
\bibcite{MR2318546}{{\v S}un07}
\bibcite{0610033}{SVV06}
\bibcite{MR1995624}{SW03}
\bibcite{MR2390328}{SZ08}
\bibcite{tan:database}{Tan02}
\bibcite{vneumann}{vN29}
\bibcite{0604328}{VV06}
\bibcite{MR2318547}{VV07}
