Process Algebras with Localities

Abstract Process algebras can be enriched with localities that explicitly describe the distribution of processes. Localities may represent physical machines, or more generally distribution units where processes are grouped according to some criterion like the sharing of resources. In a concurrent process, localities are naturally associated with (groups of) parallel components. These localities then intervene in the semantics of processes and become part, to some extent, of their observable behaviour. In a first line of research, initiated in the early nineties, localities have been used to give noninterleaving semantics for process algebras, and particularly for Milner's calculus CCS. Here localities are used to differentiate parallel components. The resulting semantics, taking into account distribution, is more discriminating than the standard interleaving semantics of the calculus. It is also incomparable with other noninterleaving semantics proposed for CCS, based on the notion of causality. More recently, localities have appeared in a number of new calculi for describing mobile processes. The idea here is that some “network awareness” is required to model wide-area distributed mobile computation. In these calculi localities are more than simple units of distribution. According to the case, they become units of failure, of communication, of migration or of security. This chapter reviews in some detail the first body of work, and tries to delineate the main ideas of the more recent studies, which are still, for the most part, at an early stage of development.