A Completion Procedure for Finitely Presented Groups That Is Based on Word Cycles

Authors:
Robert Cremanns;Friedrich Otto
Affiliations:
Fachbereich Mathematik/Informatik, Universität Kassel, D-34109 Kassel, Germany;Fachbereich Mathematik/Informatik, Universität Kassel, D-34109 Kassel, Germany e-mail: otto@theory.informatik.uni-kassel.de
Venue:
Journal of Automated Reasoning
Year:
2002

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Abstract

A Knuth–Bendix-style completion procedure for groups is presented that, instead of working with sets of string-rewriting rules, manipulates finite sets of iword cycles. A characterization is given for the resulting sets of persistent word cycles, from which it follows that the completion procedure terminates successfully if and only if the ireduced word problem of the finite group presentation considered is a finite set. In this case the resulting set of persistent word cycles yields a finite canonical string-rewriting system for every linear reduction ordering.