Cross-sections for finitely presented monoids with decidable word problems

  • Friedrich Otto
  • Masashi Katsura
  • Yuji Kobayashi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1232)


A finitely presented monoid has a decidable word problem if and only if it has a recursive cross-section if and only if it can be presented by some left-recursive convergent string-rewriting system. However, regular cross-sections or even context-free cross-sections do not suffice. This is shown by presenting examples of finitely presented monoids with decidable word problems that do not admit regular cross-sections, and that, hence, cannot be presented by left-regular convergent stringrewriting systems. Also examples of finitely presented monoids with decidable word problems are presented that do not even admit context-free cross-sections. On the other hand, it is shown that each finitely presented monoid with a decidable word problem has a finite presentation that admits a cross-section which is a Church-Rosser language.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Friedrich Otto
    • 1
  • Masashi Katsura
    • 2
  • Yuji Kobayashi
    • 3
  1. 1.Fachbereich Mathematik/InformatikUniversität KasselKassel
  2. 2.Department of Mathematics, Faculty of ScienceKyoto Sangyo UniversityKyotoJapan
  3. 3.Department of Information Science, Faculty of ScienceToho UniversityFunabashiJapan

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