Topologies, Continuity and Bisimulations
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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 mu-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 mu-calculus and its relation to the standard set-theoretic semantics.
- Theoretical Mathematics