Weak Bisimulation and Open Maps

A systematic treatment of weak bisimulation and observational congruenceon presheaf models is presented. The theory is developed withrespect to a "hiding" functor from a category of paths to observablepaths. Via a view of processes as bundles, we are able to account forweak morphisms (roughly only required to preserve observable paths)and to derive a saturation monad (on the category of presheaves overthe category of paths). Weak morphisms may be encoded as strongones via the Kleisli construction associated to the saturation monad.A general notion of weak open-map bisimulation is introduced, andresults relating various notions of strong and weak bisimulation areprovided. The abstract theory is accompanied by the concrete studyof 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 Logicin Computer science, LICS'99, IEEE Press, July 1999.