Tree Automata, Mu-Calculus and Determinacy (Extended Abstract) (original) (raw)

We show that the propositional Mu-Calculus is equivalent in expressive p o wer to nite automata on innite trees. Since complementation is trivial in the Mu-Calculus, our equivalence provides a radically simpli ed, alternative proof of Rabin's complementation lemma for tree automata, which is the heart of one of the deepest decidability results. We also show h o w Mu-Calculus can be used to establish determinacy of in nite games used in earlier proofs of complementation lemma, and certain games used in the theory of on-line algorithms.