Weak Bisimulation and Open Maps

Abstract

<p>A systematic treatment of weak bisimulation and observational congruence<br />on presheaf models is presented. The theory is developed with<br />respect to a "hiding" functor from a category of paths to observable<br />paths. Via a view of processes as bundles, we are able to account for<br />weak morphisms (roughly only required to preserve observable paths)<br />and to derive a saturation monad (on the category of presheaves over<br />the category of paths). Weak morphisms may be encoded as strong<br />ones via the Kleisli construction associated to the saturation monad.<br />A general notion of weak open-map bisimulation is introduced, and<br />results relating various notions of strong and weak bisimulation are<br />provided. The abstract theory is accompanied by the concrete study<br />of two key models for concurrency, the interleaving model of synchronisation<br /> trees and the independence model of labelled event structures.</p><p>To appear in Proceedings of the 14th Annual IEEE Symposium on Logic<br />in Computer science, LICS'99, IEEE Press, July 1999.</p><p> </p>