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Canonical Forms in Finitely Presented Algebras

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7th International Conference on Automated Deduction (CADE 1984)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 170))

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Abstract

This paper is an overview of rewriting systems as a tool to solve word problems in usual algebras. A successful completion of an equational theory, defining a variety of algebras, induces the existence of a completion procedure for the finite presentations in this variety.

The common background of these algorithms implies a unified vision of several well-known algorithms: Thue systems, abelian group decomposition, Dehn systems for small cancellation groups, Buchberger and Bergman’s algorithms, while experiments on many classical groups proove their practical efficiency despite negative decidability results.

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Author information

Authors and Affiliations

  1. INRIA, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153, Le Chesnay Cedex, France

    Philippe Le Chenadec

Authors
  1. Philippe Le Chenadec
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Editor information

Editors and Affiliations

  1. SRI International, 333 Ravenswood Avenue, Menlo Park, CA, 94025, USA

    R. E. Shostak

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© 1984 Springer-Verlag Berlin Heidelberg

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Le Chenadec, P. (1984). Canonical Forms in Finitely Presented Algebras. In: Shostak, R.E. (eds) 7th International Conference on Automated Deduction. CADE 1984. Lecture Notes in Computer Science, vol 170. Springer, New York, NY. https://doi.org/10.1007/978-0-387-34768-4_9

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  • DOI: https://doi.org/10.1007/978-0-387-34768-4_9

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96022-7

  • Online ISBN: 978-0-387-34768-4

  • eBook Packages: Springer Book Archive

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