On The Complexity of w-Automata

Automata on infinite words were introduced by Biichi in order to give a decision procedure for SlS, the monadic second-order theory of one successor. Muller suggested deterministic w-automata as a means of describing the behavior of non-stabilizing circuits. McNaughton proved that the classes of languages accepted by nondeterministic Biichi automata and by deterministic Muller automata are the same. His construction and its proof are quite complicated, and the blow-up of the construction is doubly exponential. Our main result is a new determinization construction. The advantages of the construction are that it is simpler and yields a single exponent upper bound for the general case. This construction is essentially optimal. Using the construction we can also obtain an improved complementation construction for Biichi automata, which is aIso optimaI. Both constructions can be used to improve the complexity of decision procedures that use automata-theoretic techniques.