A complete axiomatisation for observational congruence of finite-state behaviours
Information and Computation
Priorities in process algebras
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
Theoretical Computer Science
Communication and Concurrency
Priority and Maximal Progress Are Completely Axioatisable (Extended Abstract)
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
A Process Algebra with Distributed Priorities
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
Priority and Abstraction in Process Algebra
Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science
A Complete Axiomatization for Observational Congruence of Prioritized Finite-State Behaviors
A Complete Axiomatization for Observational Congruence of Prioritized Finite-State Behaviors
Electronic Notes in Theoretical Computer Science (ENTCS)
ICTAC'10 Proceedings of the 7th International colloquium conference on Theoretical aspects of computing
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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 δ 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.