Automata: from logics to algorithms

We review, in a unified framework, translations from five different logics—monadic second-order logic of one and two successors (S1S and S2S), linear-time temporal logic (LTL), computation tree logic (CTL), and modal µ-calculus (MC)—into appropriate models of finite-state automata on infinite words or infinite trees. Together with emptiness-testing algorithms for these models of automata, this yields decision procedures for these logics. The translations are presented in a modular fashion and in a way such that optimal complexity bounds for satisfiability, conformance (model checking), and realizability are obtained for all logics.

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