Algebra of communicating processes with abstraction

Abstract

We present an axiom system ACP, for communicating processes with silent actions (‘τ-steps’). The system is an extension of ACP, Algebra of Communicating Processes, with Milner's τ-laws and an explicit abstraction operator. By means of a model of finite acyclic process graphs for ACPτ, syntactic properties such as consistency and conservativity over ACP are proved. Furthermore, the Expansion Theorem for ACP is shown to carry over to ACPτ. Finally, termination of rewriting terms according to the ACPτ, axioms is probed using the method of recursive path orderings.