Abstract
The problem of complementing Büchi automata arises when developing procedures for temporal logics of programs. Unfortunately, previously known constructions for complementing Büchi automata involve a doubly exponential blow-up in the size of the automaton. We present a construction that involves only an exponential blow-up. We use this construction to prove a polynomial space upper bound for the propositional temporal logic of regular events and to prove a complexity hierarchy result for quantified propositional temporal logic.
extended abstract
Preview
Unable to display preview. Download preview PDF.
5. References
H. Alaiwan, “Equivalence of Infinite Behavior of Finite Automata”, Theoretical Computer Science 31(1984), pp. 297–306.
J. R. Büchi, “On a Decision Method in Restricted Second Order Arithmetic”, Proc. Internat. Congr. Logic, Method and Philos. Sci. 1960, Stanford University Press, 1962, pp. 1–12.
J. R. Büchi, “The Monadic Theory of ω1”, In Decidable Theories II, Lecture Notes in Mathematics, v. 328, Springer-Verlag, 1973, pp. 1–127.
Y. Choueka, “Theories of Automata on ω-Tapes: A Simplified Approach”, J. Computer and System Sciences, 8 (1974), pp. 117–141.
S. Eilenberg, Automata, Languages and Machines, vol. A, Academic Press, New York, 1974.
D. Harel, D. Kozen, R. Parikh, “Process Logic Expressiveness, Decidability, Completeness”, Journal of Computer and System Science 25, 2 (1982), pp. 144–170.
R. McNaughton, “Testing and Generating Infinite Sequences by a Finite Automaton”, Information and Control 9 (1966), pp. 521–530
A. R. Meyer, “Weak Monadic Second Order Theory of Successor is not Elementary Recursive”, Proc. Logic Colloquium, Lecture Notes in Mathematics, v. 453, Springer-Verlag, 1975, pp. 132–154.
A. R. Meyer, L. J. Stockmeyer, “The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Time”, Proc. 13th IEEE Symp. on Switching and Automata Theory, Long Beach, CA, 1972, pp. 125–129.
H. Nishimura, “Descriptively Complete Process Logic”, Acta Informatica, 14 (1980), pp. 359–369.
A. Pnueli, “The Temporal Logic of Concurrent Programs”, Theoretical Computer Science 13(1981), pp. 45–60.
M.O. Rabin, “Decidability of Second Order Theories and Automata on Infinite Trees”, Trans. AMS, 141(1969), pp. 1–35.
M.O. Rabin, “Weakly Definable Relations and Special Automata”, Proc. Symp. Math. Logic and Foundations of Set Theory (Y. Bar-Hillel, ed.), North-Holland, 1970, pp. 1–23.
E. L. Robertson, “Structure of Complexity in the Weak Monadic Second-Order Theory of the Natural Numbers”, Proc. 6th ACM Symp. on Theory of Computing, Seattle, 1974, pp. 161–171.
M. O. Rabin, D. Scott, “Finite Automata and their Decision Problems”, IBM J. Res. & Dev., 3(2), 1959, pp 114–125.
A.P. Sistla, E.M. Clarke, “The Complexity of Propositional Linear Time Logics”, Proc. 14th ACM Symp. on Theory of Computing, San Francisco, 1982, pp. 159–168, to appear in J. ACM.
D. Siefkes, Decidable Theories I — Büchi's Monadic Second-Order Successor Arithmetics, Lecture Notes in Mathematics, v. 120, Springer-Verlag, 1970.
A. P. Sistla, Theoretical Issues in The Design and Verification of Distributed Systems, Ph.D. Thesis, Harvard University, 1983.
B. A. Trakhtenbrot, Y. M. Barzdin, Finite Automata Behavior and Synthesis, North Holland, Amsterdam, 1973.
M.Y. Vardi, “On deterministic ω-automata”, to appear.
M.Y. Vardi, L. Stockmeyer, “Improved Upper and Lower Bounds for Modal Logics of Programs”, Proc. 17 ACM Symp. on Theory of Computing, Providence, May 1985.
M. Y. Vardi, P. Wolper, “Yet Another Process Logic”, in Logics of Programs, Springer-Verlag Lecture Notes in Computer Science, vol. 164, Berlin, 1983, pp. 501–512.
M. Y. Vardi, P. Wolper, “Automata Theoretic Techniques for Modal Logics of Programs”, IBM Research Report, October 1984. A preleminary version appeared in Proc. ACM Symp. on Theory of Computing, Washington, April 1984, pp. 446–456.
P. Wolper, M. Y. Vardi, A. P. Sistla, “Reasoning about Infinite Computation Paths”, Proc. 24th IEEE Symp. on Foundations of Computer Science, Tucson, 1983, pp. 185–194.
P. Wolper, “Synthesis of Communicating Processes from Temporal Logic Specifications”, Ph. D. Thesis, Stanford University, 1982.
P. Wolper, “Temporal Logic Can Be More Expressive”, Information and Control, 56(1983), pp. 72–99.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sistla, A.P., Vardi, M.Y., Wolper, P. (1985). The complementation problem for Büchi automata with applications to temporal logic. In: Brauer, W. (eds) Automata, Languages and Programming. ICALP 1985. Lecture Notes in Computer Science, vol 194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015772
Download citation
DOI: https://doi.org/10.1007/BFb0015772
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15650-5
Online ISBN: 978-3-540-39557-7
eBook Packages: Springer Book Archive