On &ohgr;-automata and temporal logic
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Co-ing Büchi Made Tight and Useful
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
From LTL to symbolically represented deterministic automata
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Alternation removal in büchi automata
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
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CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Tightening the exchange rates between automata
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Translating to Co-Büchi Made Tight, Unified, and Useful
ACM Transactions on Computational Logic (TOCL)
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We solve the open problems of translating, when possible, all common classes of nondeterministic word automata to deterministic and nondeterministic co-Büchi word automata. The handled classes include Büchi, parity, Rabin, Streett and Muller automata. The translations follow a unified approach and are all asymptotically tight. The problem of translating Büchi automata to equivalent co-Büchi 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 Büchi 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 Büchi word automata.