Presheaf Models for CCS-like Languages

Abstract

The aim of this paper is to harness the mathematical machinery around<br />presheaves for the purposes of process calculi. Joyal, Nielsen and Winskel<br />proposed a general definition of bisimulation from open maps. Here we show<br />that open-map bisimulations within a range of presheaf models are congruences<br /> for a general process language, in which CCS and related languages<br />are easily encoded. The results are then transferred to traditional models<br /> for processes. By first establishing the congruence results for presheaf<br />models, abstract, general proofs of congruence properties can be provided<br />and the awkwardness caused through traditional models not always possessing<br /> the cartesian liftings, used in the break-down of process operations,<br />are side-stepped. The abstract results are applied to show that hereditary<br />history-preserving bisimulation is a congruence for CCS-like languages to<br />which is added a refinement operator on event structures as proposed by<br />van Glabbeek and Goltz.