Using groups for investigating rewrite systems

We describe several technical tools that prove to be efficient for investigating the rewrite systems associated with an equational specification. These tools consist in introducing a monoid of partial maps, listing the monoid relations corresponding to the local confluence diagrams of the rewrite system, then introducing the group presented by these relations, and finally replacing the initial rewrite system with a internal process entirely sitting in the latter 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 such techniques can be useful for more general rewrite systems.

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Patrick Dehornoy
• Keywords: CORR 2006, Education, Initial Rewrite, Local Confluence Diagrams, Rewrite Systems