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Using groups for investigating rewrite systems

Published online by Cambridge University Press:  01 December 2008

PATRICK DEHORNOY  and
VINCENT VAN OOSTROM
PATRICK DEHORNOY
Affiliation:
Laboratoire de Mathématiques Nicolas Oresme, Université de Caen, 14032 Caen, France Email: [email protected] Website: www.math.unicaen.fr/ dehornoy
VINCENT VAN OOSTROM
Affiliation:
Universiteit Utrecht, Heidelberglaan 6, 3584CS Utrecht, Netherlands Email: [email protected] Website: www.phil.uu.nl/ oostrom
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Abstract

We describe several technical tools that prove to be efficient for investigating the rewrite systems associated with an equational specification. These tools consist of introducing a monoid of partial maps, listing the monoid relations corresponding to the local confluence diagrams of the rewrite system, introducing the group presented by these relations, and, finally, replacing the initial rewrite system with an internal process entirely sitting in this group. When the approach can be completed, one typically obtains a practical method for constructing algebras satisfying prescribed equations and for solving the associated word problem. The above techniques have been developed by the first author in a context of general algebra. The goal of this paper is to bring them to the attention of the rewrite system community. We hope that these techniques may be useful for more general rewrite systems.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 18 , Issue 6 , December 2008 , pp. 1133 - 1167
Copyright
Copyright © Cambridge University Press 2008

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