A Complete Axiomatisation for Observational Congruence of Finite-State Behaviors

Abstract Finite state automata, with non-determinism and silent transitions, can be interpreted not as subsets of the free monoid as in classical automata theory, but as congruence classes under a congruence relation based upon the notion of weak bisimulation or observational equivalence due to Park and Milner. In this paper a complete axiomatisation for this congruence is presented. It extends the previously known complete axiomatisation by Hennessy and Milner for the case when all computations are finite; the extension consists of five simple rules for recursion.

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