Weak Bisimulation and Open Maps

Abstract

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.