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The problem of complementing Büchi automata arises when developing decision procedures for temporal logics of programs. Unfortunately, previously known constructions for complementing Büchi automata involve a doubly exponential blow-up in the size of the automaton. We present a construction that involves only an exponential blow-up. We use this construction to prove a polynomial space upper bound for the propositional temporal logic of regular events and to prove a complexity hierarchy result for quantified propositional temporal logic.

In this paper, we consider the model checking problem for the μ-calculus and show that it is succinctly equivalent to the non-emptiness problem of finite-state automata on infinite binary trees with the parity acceptance condition. We also present efficient model checking algorithms for two rich subclasses of the μ-calculus formulas and relate their expressive power to well-known extensions of branching time temporal logics.