Unification and matching in process algebras

Abstract

We consider the compatibility checking problem for a simple fragment of CCS, called BCCSP[12], using equational unification techniques. Two high-level specifications given as two process algebraic terms with free variables are said to be compatible modulo some equivalence relation if a substitution on the free variables can make the resulting terms equivalent modulo that relation. We formulate this compatibility (modulo an equivalence relation) checking problems as unification problems in the equational theory of the the corresponding equivalence relation. We use van Glabbeek's equational axiomatizations [12] for some interesting process algebraic relations. Specifically, we consider equational axiomatizations for bisimulation equivalence and trace equivalence and establish complexity lower bounds and upper bounds for the corresponding unification and matching problems. We also show some special cases for which efficient algorithmic solutions exist.