  
  
                                    [1X kbmag [101X
  
  
                 [1X Knuth-Bendix on Monoids and Automatic Groups [101X
  
  
                                     1.5.9
  
  
                                  7 July 2019
  
  
                                   Derek Holt
  
  
  
  Derek Holt
      Email:    [7Xmailto:D.F.Holt@warwick.ac.uk[107X
      Homepage: [7Xhttps://homepages.warwick.ac.uk/staff/D.F.Holt/[107X
      Address:  [33X[0;14YMathematics Institute[133X
                [33X[0;14YUniversity of Warwick[133X
                [33X[0;14YCoventry CV4 7AL[133X
                [33X[0;14YUK[133X
  
  
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThe  [5XKBMag[105X  package  is a [5XGAP[105X interface to some `C' programs for running the
  Knuth-Bendix  completion  program  on  finite  semigroup,  monoid  or  group
  presentations,  and  for  attempting  to  compute  automatic  structures  of
  finitely presented groups.[133X
  
  [33X[0;0YBug  reports,  comments,  suggestions for additional features, and offers to
  implement some of these, will all be very welcome.[133X
  
  [33X[0;0YPlease submit any issues at [11Xhttps://github.com/gap-packages/kbmag/issues/[111X.[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 1997 by Derek Holt[133X
  
  [33X[0;0YThis  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 2.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YThis  documentation  was  prepared with the [5XGAPDoc[105X [LN17] and [5XAutoDoc[105X [GH17]
  packages.[133X
  
  [33X[0;0YThe   procedure   used   to   produce   new   releases   uses   the  package
  [5XGitHubPagesForGAP[105X [Hor17] and the package [5XReleaseTools[105X.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (kbmag)[101X
  
  1 [33X[0;0YIntroduction[133X
  2 [33X[0;0YThe Knuth-Bendix program on semigroups, monoids and groups[133X
    2.1 [33X[0;0YCreating a rewriting system[133X
      2.1-1 KBMAGRewritingSystem
    2.2 [33X[0;0YElementary functions on rewriting systems[133X
      2.2-1 IsKBMAGRewritingSystemRep
      2.2-2 IsConfluent
      2.2-3 SemigroupOfRewritingSytem
      2.2-4 ExternalWordToInternalWordOfRewritingSystem
      2.2-5 Alphabet
      2.2-6 Rules
      2.2-7 ResetRewritingSystem
    2.3 [33X[0;0YSetting the ordering[133X
      2.3-1 SetOrderingOfKBMAGRewritingSystem
    2.4 [33X[0;0YControl parameters[133X
      2.4-1 InfoRWS
      2.4-2 OptionsRecordOfKBMAGRewritingSystem
    2.5 [33X[0;0YThe Knuth-Bendix program[133X
      2.5-1 KnuthBendix
      2.5-2 ReductionAutomaton
    2.6 [33X[0;0YThe automatic groups program[133X
      2.6-1 AutomaticStructure
      2.6-2 WordAcceptor
    2.7 [33X[0;0YWord reduction[133X
      2.7-1 IsReducedWord
      2.7-2 ReducedWord
    2.8 [33X[0;0YCounting and enumerating irreducible words[133X
      2.8-1 Size
      2.8-2 Order
      2.8-3 EnumerateReducedWords
      2.8-4 GrowthFunction
    2.9 [33X[0;0YRewriting System Examples[133X
      2.9-1 [33X[0;0YExample 1[133X
      2.9-2 [33X[0;0YExample 2[133X
      2.9-3 [33X[0;0YExample 3[133X
      2.9-4 [33X[0;0YExample 4[133X
      2.9-5 [33X[0;0YExample 5[133X
  3 [33X[0;0YThe Knuth-Bendix program on cosets[133X
    3.1 [33X[0;0YSubgroups, cosets and subgroup presentations[133X
      3.1-1 SubgroupOfKBMAGRewritingSystem
      3.1-2 ResetRewritingSystemOnCosets
    3.2 [33X[0;0YThe Knuth-Bendix program on cosets[133X
      3.2-1 KnuthBendixOnCosets
      3.2-2 RewritingSystemOfSubgroupOfKBMAGRewritingSystem
      3.2-3 IsConfluentOnCosets
    3.3 [33X[0;0YThe automatic cosets program[133X
      3.3-1 AutomaticStructureOnCosets
      3.3-2 PresentationOfSubgroupOfKBMAGRewritingSystem
    3.4 [33X[0;0YWord reduction on cosets[133X
      3.4-1 IsReducedCosetRepresentative
      3.4-2 ReducedCosetRepresentative
    3.5 [33X[0;0YCounting and enumerating irreducible words for cosets[133X
      3.5-1 Index
      3.5-2 EnumerateReducedCosetRepresentatives
      3.5-3 GrowthFunctionOfCosetRepresentatives
    3.6 [33X[0;0YExamples of the use of Rewriting System on Cosets[133X
      3.6-1 [33X[0;0YExample 1[133X
      3.6-2 [33X[0;0YExample 2[133X
  4 [33X[0;0YThe stand-alone package[133X
    4.1 [33X[0;0YFunctions for manipulating finite state automata[133X
      4.1-1 IsInitializedFSA
      4.1-2 InitializeFSA
      4.1-3 FSA
      4.1-4 WriteFSA
      4.1-5 IsDeterministicFSA
      4.1-6 AlphabetFSA
      4.1-7 NumberOfStatesFSA
      4.1-8 NumberOfLettersFSA
      4.1-9 AcceptingStatesFSA
      4.1-10 InitialStatesFSA
      4.1-11 DenseDTableFSA
      4.1-12 SparseTableFSA
      4.1-13 TargetDFA
      4.1-14 TargetsFSA
      4.1-15 SourcesFSA
      4.1-16 WordTargetDFA
      4.1-17 IsAcceptedWordDFA
      4.1-18 AddStateFSA
      4.1-19 DeleteStateFSA
      4.1-20 PermuteStatesFSA
      4.1-21 AddLetterFSA
      4.1-22 DeleteLetterFSA
      4.1-23 PermuteLettersFSA
      4.1-24 AddEdgeFSA
      4.1-25 DeleteEdgeFSA
      4.1-26 SetAcceptingFSA
      4.1-27 SetInitialFSA
      4.1-28 IsAccessibleFSA
      4.1-29 AccessibleFSA
      4.1-30 IsTrimFSA
      4.1-31 TrimFSA
      4.1-32 IsBFSFSA
      4.1-33 BFSFSA
      4.1-34 LSizeDFA
      4.1-35 LEnumerateDFA
    4.2 [33X[0;0YFunctions calling external programs[133X
      4.2-1 DeterminizeFSA
      4.2-2 MinimizeFSA
      4.2-3 NotFSA
      4.2-4 StarFSA
      4.2-5 ReverseFSA
      4.2-6 ExistsFSA
      4.2-7 SwapCoordsFSA
      4.2-8 AndFSA
      4.2-9 OrFSA
      4.2-10 ConcatFSA
      4.2-11 LanguagesEqualFSA
      4.2-12 GrowthFSA
  
  
  [32X
