The word problem for finitely presented monoids and finite canonical rewriting systems

  • Craig Squier
  • Friedrich Otto
Theoretical Aspects 1
Part of the Lecture Notes in Computer Science book series (LNCS, volume 256)


The main purpose of this paper is to describe a negative answer to the following question:

Does every finitely presented monoid with a decidable word problem have a presentation (∑;R) where R is a finite canonical rewriting system?

To obtain this answer a certain homological finiteness condition for monoids is considered. If M is a monoid that can be presented by a finite canonical rewriting system, then M is an (FP)3-monoid. Since there are well-known examples of finitely presented groups that have easily decidable word problem, but that do not meet this condition, this implies that there are finitely presented monoids (and groups) with decidable word problem that cannot be presented by finite canonical rewriting systems.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Craig Squier
    • 1
  • Friedrich Otto
    • 2
  1. 1.Department of MathematicsState University of New YorkBinghamtonUSA
  2. 2.Fachbereich InformatikUniversitaet KaiserslauternKaiserslauternGermany

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