Locality based semantics for process algebras

A general framework proposed by Degano, De Nicola and Montanari has been fruitful to define in a natural way non interleaving semantics for process description languages based on causality. The framework relies on a decomposition function used to obtain the set of its sequential processes from a parallel term, and on a set of distributed transition rules carrying information about the actions processes can perform and their location. In this paper we show that also semantics discriminating according to space distribution of processes can be formulated in a natural way within this framework. Two new semantics are proposed. The first one is based on an alternative characterization of the locality equivalence of Boudol, Castellani, Hennessy and Kiehn. Over the latter, our equivalence has the advantage of not requiring explicit introduction of a (infinite) space of locations; this makes it amenable to a mechanical treatment in the same vein as the classical bisimulation-based equivalences. The second semantics is proposed via a direct generalization of Castellani and Hennessy's distributed equivalence to languages with global scoping operators.