Open AccessWeak Bisimulation and Open Maps
Author(s) -
Marcelo Fiore,
Gian Luca Cattani,
Glynn Winskel
Publication year - 1999
Publication title -
brics report series
Language(s) - English
Resource type - Journals
eISSN - 1601-5355
pISSN - 0909-0878
DOI - 10.7146/brics.v6i14.20071
Subject(s) - bisimulation , functor , mathematics , morphism , concurrency , monad (category theory) , congruence (geometry) , discrete mathematics , observable , pure mathematics , computer science , programming language , physics , geometry , quantum mechanics
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.