Bisimulations and Behaviour of Nondeterministic Automata

Abstract

The minimization of nondeterministic automata without initial states (developed within a game-theoretic framework in Calude, Calude, Khoussainov [3]) is presented in terms of bisimulations; the minimal automaton is unique up to an isomorphism in case of reversible automata. We also prove that there exists an in nite class of (strongly connected) nondeterministic automata each of which is not bisimilar with any deterministic automaton. This shows that in the sense of bisimilarity nondeterministic automata are more powerful than deterministic ones. It is an open question whether the method of bisimulations can produced, in general, the unique minimal nondeterministic automaton.