Since Edward Moore, finite automata theory has been inspired by physics, in particular by quantum complementarity. We review automaton complementarity, reversible automata and the connections to generalized urn models. Recent developments in quantum information theory may have appropriate formalizations in the automaton context.

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 infinite 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.