On Coherence Properties in Term Rewriting Models of Concurrency

Abstract

This paper introduces a generic and uniform approach to integrate different design languages for distributed systems in verification tools. It is based on Meseguer’s Rewriting Logic, hence transitions between the states of the respective system are modeled as (conditional) term rewriting steps modulo an equational theory. We argue that, for reasons of efficiency, it is intractable to admit arbitrary equations, and propose to employ rewriting modulo associativity and commutativity instead, using oriented versions of the equations. Furthermore the question is raised under which conditions this implementational restriction is complete. To this aim we define a coherence property which guarantees that every transition which is possible in the (fully equational) semantics can also be computed using the oriented equations, and we show that this property can be verified by testing the joinability of finitely many conditional critical pairs between transition rules and oriented equations.