Analysis of Dehn's algorithm by critical pairs
Theoretical Computer Science
Handbook of theoretical computer science (vol. B)
String-rewriting systems
Unification of infinite sets of terms schematized by primal grammars
Theoretical Computer Science
Term Rewriting Systems
The Unification of Infinite Sets of Terms and Its Applications
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
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We introduce parameterized rewrite systems for describing infinite families of finite string rewrite systems depending upon non-negative integer parameters, as well as ways to reason uniformly over these families. Unlike previous work, the vocabulary on which a rewrite system in the family is built depends itself on the integer parameters. Rewriting makes use of a toolkit for parameterized words which allows to describe a rewrite step made independently by all systems in an infinite family by a single, effective parameterized rewrite step. The main result is a confluence test for all systems in a family at once, based on a critical pair lemma classically based on computing finitely many overlaps between left-hand sides of parameterized rules and then checking for their joinability (which decidability is not garanteed).