Co-Büching Them All

We solve the open problems of translating, when possible, all common classes of nondeterministic word automata to deterministic and nondeterministic co-Buchi word automata. The handled classes include Buchi, parity, Rabin, Streett and Muller automata. The translations follow a unified approach and are all asymptotically tight. The problem of translating Buchi automata to equivalent co-Buchi automata was solved in [2], leaving open the problems of translating automata with richer acceptance conditions. For these classes, one cannot easily extend or use the construction in [2]. In particular, going via an intermediate Buchi automaton is not optimal and might involve a blow-up exponentially higher than the known lower bound. Other known translations are also not optimal and involve a doubly exponential blow-up. We describe direct, simple, and asymptotically tight constructions, involving a 2Θ(n) blow-up. The constructions are variants of the subset construction, and allow for symbolic implementations. Beyond the theoretical importance of the results, the new constructions have various applications, among which is an improved algorithm for translating, when possible, LTL formulas to deterministic Buchi word automata.

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