Automata theoretic techniques for modal logics of programs (extended abstract)

We present a new technique for obtaining decision procedures for modal logics of programs. The technique centers around a new class of finite automata on infinite trees for which the emptiness problem can be solved in polynomial time. The decision procedures then consist of constructing an automaton Af for a given formula f, such that Af accepts some tree if and only if f is satisfiable. We illustrate our technique by giving an exponential decision procedure for deterministic propositional dynamic logic and a variant of the μ-calculus of Kozen.