Automata-Theoretic techniques for modal logics of programs
Journal of Computer and System Sciences
Complementing deterministic Bu¨chi automata in polynomial time
Journal of Computer and System Sciences
On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Reasoning about infinite computations
Information and Computation
Computer-aided verification of coordinating processes: the automata-theoretic approach
Computer-aided verification of coordinating processes: the automata-theoretic approach
A Comparative Study of Symbolic Algorithms for the Computation of Fair Cycles
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
Deterministic w Automata vis-a-vis Deterministic Buchi Automata
ISAAC '94 Proceedings of the 5th International Symposium on Algorithms and Computation
The ForSpec Temporal Logic: A New Temporal Property-Specification Language
TACAS '02 Proceedings of the 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
CTL+ is Exponentially more Succinct than CTL
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
From linear time to branching time
ACM Transactions on Computational Logic (TOCL)
Reasoning about infinite computation paths
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
On the complexity of omega -automata
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
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
The quest for a tight translation of büchi to co-büchi automata
Fields of logic and computation
Translating to Co-Büchi Made Tight, Unified, and Useful
ACM Transactions on Computational Logic (TOCL)
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The practical importance of automata on infinite objects has motivated a re-examination of the complexity of automata-theoretic constructions. One such construction is the translation, when possible, of nondeterministic Büchi word automata (NBW) to nondeterministic co-Büchi word automata (NCW). Among other applications, it is used in the translation (when possible) of LTL to the alternation-free μ -calculus. The best known upper bound for the translation of NBW to NCW is exponential (given an NBW with n states, the best translation yields an equivalent NCW with 2 O (n logn ) states). On the other hand, the best known lower bound is trivial (no NBW with n states whose equivalent NCW requires even n + 1 states is known). In fact, only recently was it shown that there is an NBW whose equivalent NCW requires a different structure. In this paper we improve the lower bound by showing that for every integer k ≥ 1 there is a language L k over a two-letter alphabet, such that L k can be recognized by an NBW with 2k + 1 states, whereas the minimal NCW that recognizes L k has 3k states. Even though this gap is not asymptotically very significant, it nonetheless demonstrates for the first time that NBWs are more succinct than NCWs. In addition, our proof points to a conceptual advantage of the Büchi condition: an NBW can abstract precise counting by counting to infinity with two states. To complete the picture, we consider also the reverse NCW to NBW translation, and show that the known upper bound, which duplicates the state space, is tight.