Canonical Forms in Finitely Presented Algebras

  • Philippe Le Chenadec
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 170)


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.


Finitely Presented Algebras Word Problem Rewriting Systems Completion Procedures 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Philippe Le Chenadec
    • 1
  1. 1.INRIADomaine de VoluceauLe Chesnay CedexFrance

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