A Complete Axiomatization for Observational Congruence of Prioritized Finite-State Behaviors

Abstract

Milner’s complete proof system for observational congruence is crucially based on the possibility to equate τ divergent expressions to non-divergent ones by means of the axiom recX.(τ.X + E) = recX.τ.E. In the presence of a notion of priority, where e.g. actions of type δ have a lower priority than silent τ actions, this axiom is no longer sound because a τ action performable by E is pre-empted in the left-hand term but not in the right-hand term. The problem of axiomatizing priority using the standard observational congruence has been open for a long time. Here we show that this can be done by introducing an auxiliary operator pri(E), by suitably modifying the axiom above and by introducing some new axioms. Our technique provides a complete axiomatization for Milner’s observational congruence over finite-state terms of a process algebra with priority and recursion.