Axiomatizing weak simulation semantics over BCCSP

Abstract

Abstract. This paper is devoted to the study of the (in)equational theory of the largest (pre)congruences over the language BCCSP induced by variations on the classic simulation preorder and equivalence that abstract from internal steps in process behaviours. In particular, the article focuses on the (pre)congruences associated with the weak simulation, the weak complete simulation and the weak ready simulation preorders. For each of these behavioural semantics, results on the (non)existence of finite (ground-)complete (in)equational axiomatizations are given. The axiomatization of those semantics using conditional equations is also discussed in some detail.

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“…It is one of important topics in concurrency theory that giving axiomatization for behaviour relations. For example, Milner gives an axiomatization for observational congruence in CCS [19]; Baeten and Bravetti extend Milner's this work and provide an axiomatization over TCP+REC f [2], where TCP+REC f is a fragment of TCP+REC which is a generic process language that embodies features of the classical process algebras CCS, CSP and ACP; Lin offers complete inference systems for late and early weak bisimulation equivalences for processes without involving recursion in π-calculus [14]; Aceto et al explore the axiomatization of weak simulation semantics systematically over BCCSP (without recursion) [1]. Although Lüttgen and Vogler's original paper [16] mentions some sound laws, a complete set of axioms seems out of reach.…”

The Algebra of Nondeterministic Finite Automata

“…Future research may be devoted to extend the axiomatic theory of SFM1 to other behavioral equivalences in the linear-time/branchingtime spectrum [10,11]. For instance, we claim that weak simulation equivalence [24,1] can be axiomatized by replacing axiom T2 in the set W with the axiom T2 ′ a. (x + y) = a.…”

In search of lost time: Axiomatising parallel composition in process algebras

“…Weak behavioural semantics have been introduced to study the effects of these unobservable (or silent) actions on the observable behaviour of processes, each semantics considering a different level of abstraction. A taxonomy of weak semantics is given in [44], and studies on the equational theories of various of these semantics have been carried out over the algebra BCCSP (see, among others, [15,35,49,53,63]). A finite, ground-complete axiomatisation of parallel composition modulo rooted weak bisimilarity (also known as observational congruence) is provided by Bergstra and Klop in [24] over the algebra ACP τ that, however, includes the auxiliary operators and |.…”