Open maps as a bridge between algebraic observational equivalence and bisimilarity

Abstract

We show that observational equivalences for standard, partial and regular algebras are bisimulation equivalences in the setting of open maps, proposed in [JNW93] as an abstract approach to behavioural equivalences of processes. The main advantage of the results is capturing models for sequential and concurrent systems in a uniform framework. In such an abstract setting we formulate the property of determinism, shared by all the algebras considered in this paper, and identify some interesting facts about bisimilarity in the deterministic case. All the results for standard, regular and partial algebras are obtained by the applications of general theorems proved in the paper, which we expect to be applicable also in other contexts.