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International Conference on Rewriting Techniques and Applications

RTA 1987: Rewriting Techniques and Applications pp 74–82Cite as

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

Theoretical Aspects 1

Part of the Lecture Notes in Computer Science book series (LNCS,volume 256)

Abstract

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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Author notes

  1. Friedrich Otto

    Present address: Department of Computer Science, State University of New York, 12222, Albany, N.Y., USA

Authors and Affiliations

  1. Department of Mathematics, State University of New York, 13901, Binghamton, N.Y., USA

    Craig Squier

  2. Fachbereich Informatik, Universitaet Kaiserslautern, Postfach 3049, 6750, Kaiserslautern, Germany

    Friedrich Otto

Authors
  1. Craig Squier
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  2. Friedrich Otto
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    © 1987 Springer-Verlag Berlin Heidelberg

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    Squier, C., Otto, F. (1987). The word problem for finitely presented monoids and finite canonical rewriting systems. In: Lescanne, P. (eds) Rewriting Techniques and Applications. RTA 1987. Lecture Notes in Computer Science, vol 256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17220-3_7

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    • DOI: https://doi.org/10.1007/3-540-17220-3_7

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    • Publisher Name: Springer, Berlin, Heidelberg

    • Print ISBN: 978-3-540-17220-8

    • Online ISBN: 978-3-540-47421-0

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