Characterizing Bisimulation Congruence in the {Calculus

This paper presents a new characterization of the bisimulation congruence and D{bisimulation equivalences of the {calculus. The characterization supports a bisimulation{like proof technique which avoids explicit case analysis by taking a dynamic point of view of actions a process may perform , thus providing a new way of proving bisimulation congruence. The semantic theory of the {calculus is presented here without the notion of {equivalence. 1 Motivation The {calculus, introduced in MPW92a], presents a model of concurrent computation based upon the notion of naming. It can be seen as an extension of the theory of CCS Mil89] (and other similar process algebras) in that names (references) are the subject of communication. This introduces mobility into process algebras. Such an extension allows us to clearly express many fundamental programming features which could at best be described indirectly in CCS. The theory of CCS has been quite successful for specifying and verifying concurrent systems. The success is due to a solid equality theory based on the notion of bisimulation Par81, Mil89]. Bisimulation has many nice properties. It induces a congruence relation for CCS constructions, thus supporting compositionality. It admits a very pleasant proof technique based on xed point induction Par81]. The proof technique not only provides a means of establishing the equality theory but also opens up a direct way of program veriication. 1 Corresponding to the bisimulation equivalence in CCS, there are two main equalities in the {calculus: ground bisimulation equivalence and bisimulation congruence. The notion of ground bisimulation is a natural generalization of that of bisimulation in CCS with a pleasant proof technique. However, ground bisimula-tion equivalence is not a congruence relation for {calculus constructions, because now names are subject to substitution and ground bisimulation equivalence is not preserved under substitution of names. To obtain a congruence relation, bisimu-lation congruence is deened such that two processes are related just in case they are ground bisimilar under all substitutions. Although this immediately gives us a congruence relation, this deenition does not suggest any direct proof technique to establish congruence between processes other than tedious exhaustive case analysis. Thus, in extending CCS to the {calculus, the nice feature of proof technique is somewhat lost for bisimulation congruence | the more important relation between {calculus processes. In fact there is a whole series of distinction bisimulation equivalences such that two processes are D{bisimilar just in case they are ground bisimilar under all substitutions …