Topologies, continuity and bisimulations

-The notion of a bisimulation relation is of basic importance in many areas of computation theory and logic. Of late, it has come to take a particular significance in work on the formal analysis and verification of hybrid control systems, based on the modal //-calculus. Our purpose here is to give an analysis of the concept, starting with the observation that the zig-zag conditions are suggestive of some form of continuity. We give a topological characterization of bisimularity for preorders, and then use the topology as a route to examining the algebraic semantics for the //-calculus, developed in recent work of Kwiatkowska et al, and its relation to the standard set-theoretic semantics. 'Research supported by the ARO under the MURI program "Integrated Approach to Intelligent Systems", grant no. DAA H04-96-1-0341.