Weak Bisimulation and Open Maps

A systematic treatment of weak bisimulation and observational congruence on presheaf models is presented. The theory is developed with respect to a “hiding” functor from a category of paths to observable paths. Via a view of processes as bundles , we are able to account for weak morphisms (roughly only required to preserve observable paths) and to derive a saturation monad (on the category of presheaves over the category of paths). Weak morphisms may be encoded as strong ones via the Kleisli construction associated to the saturation monad. A general notion of weak open-map bisimulation is introduced, and results relating various notions of strong and weak bisimulation are provided. The abstract theory is accompanied by the concrete study of two key models for concurrency, the interleaving model of synchronisation trees and the independence model of labelled event structures. To appear in Proceedings of the 14th Annual IEEE Symposium on Logic in Computer science, LICS’99, IEEE Press, July 1999. This author is supported by EPSRC grant GR/L62290: Calculi for Interactive Systems: Theory and Experiment. † Basic Research in Computer Science, a centre of the Danish National Research Foundation.