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Rewrite systems for varieties of semigroups

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10th International Conference on Automated Deduction (CADE 1990)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 449))

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Abstract

We consider term and word rewriting systems for semigroup theories and study the connection between these two concepts. As an application, the lattice of all varieties of idempotent semigroups is investigated with the following point of view: Can we decide the word problem of the varieties in question by using finite canonical term or word rewriting systems ? In spite of the fact that there are infinitely many varieties of idempotent semigroups, this question can be solved completely. We thus obtain infinitely many examples of equational theories which satisfy the following property: The theory has decidable word problem, but it cannot be decided by using a finite canonical term or word rewriting system.

This research was done while the author was still at the IMMD 1, University Erlangen.

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References

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Author information

Authors and Affiliations

  1. German Research Center for Artificial Intelligence, DFKI, Projektgruppe WINO, Postfach 2080, D-6750, Kaiserslautern, West Germany

    Franz Baader

Authors
  1. Franz Baader
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Mark E. Stickel

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© 1990 Springer-Verlag Berlin Heidelberg

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Baader, F. (1990). Rewrite systems for varieties of semigroups. In: Stickel, M.E. (eds) 10th International Conference on Automated Deduction. CADE 1990. Lecture Notes in Computer Science, vol 449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52885-7_102

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  • DOI: https://doi.org/10.1007/3-540-52885-7_102

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52885-2

  • Online ISBN: 978-3-540-47171-4

  • eBook Packages: Springer Book Archive

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