Abstract
The Büchi acceptance condition specifies a set α of states, and a run is accepting if it visits α infinitely often. The co-Büchi acceptance condition is dual, thus a run is accepting if it visits α only finitely often. Nondeterministic Büchi automata over words (NBWs) are strictly more expressive than nondeterministic co-Büchi automata over words (NCWs). The problem of the blow-up involved in the translation (when possible) of an NBW to an NCW has been open for several decades.
Until recently, the best known upper bound was 2O(nlogn) and the best lower bound was n. We describe the quest to the tight 2Θ(n) bound.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Accellera: Accellera organization inc. (2006), http://www.accellera.org
Aminof, B., Kupferman, O., Lev, O.: On the relative succinctness of nondeterministic Büchi and co-Büchi word automata. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 183–197. Springer, Heidelberg (2008)
Boker, U., Kupferman, O.: Co-ing Büchi made tight and useful. In: Proc. 24th IEEE Symp. on Logic in Computer Science (2009)
Boker, U., Kupferman, O., Rosenberg, A.: Alternation removal in Büchi automata. In: Proc. 37th Int. Colloq. on Automata, Languages, and Programming (2010)
Büchi, J.R.: On a decision method in restricted second order arithmetic. In: Proc. Int. Congress on Logic, Method, and Philosophy of Science, pp. 1–12. Stanford University Press, Stanford (1962)
Emerson, E., Jutla, C.: The complexity of tree automata and logics of programs. In: Proc. 29th IEEE Symp. on Foundations of Computer Science, pp. 328–337 (1988)
Gentilini, R., Piazza, C., Policriti, A.: Computing strongly connected components in a linear number of symbolic steps. In: 14th ACM-SIAM Symp. on Discrete Algorithms, pp. 573–582 (2003)
Krishnan, S., Puri, A., Brayton, R.: Deterministic ω-automata vis-a-vis deterministic Büchi automata. In: Du, D.-Z., Zhang, X.-S. (eds.) ISAAC 1994. LNCS, vol. 834, pp. 378–386. Springer, Heidelberg (1994)
Kupferman, O.: Tightening the exchange rate beteen automata. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 7–22. Springer, Heidelberg (2007)
Kupferman, O., Lustig, Y., Vardi, M.: On locally checkable properties. In: Hermann, M., Voronkov, A. (eds.) LPAR 2006. LNCS (LNAI), vol. 4246, pp. 302–316. Springer, Heidelberg (2006)
Kupferman, O., Morgenstern, G., Murano, A.: Typeness for ω-regular automata. International Journal on the Foundations of Computer Science 17, 869–884 (2006)
Kupferman, O., Vardi, M.: From linear time to branching time. ACM Transactions on Computational Logic 6, 273–294 (2005)
Kurshan, R.: Computer Aided Verification of Coordinating Processes. Princeton Univ. Press, Princeton (1994)
Landweber, L.: Decision problems for ω–automata. Mathematical Systems Theory 3, 376–384 (1969)
McNaughton, R.: Testing and generating infinite sequences by a finite automaton. Information and Control 9, 521–530 (1966)
Miyano, S., Hayashi, T.: Alternating finite automata on ω-words. Theoretical Computer Science 32, 321–330 (1984)
Morgenstern, A., Schneider, K.: From LTL to symbolically represented deterministic automata. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds.) VMCAI 2008. LNCS, vol. 4905, pp. 279–293. Springer, Heidelberg (2008)
Piterman, N.: From nondeterministic Büchi and Streett automata to deterministic parity automata. In: Proc. 21st IEEE Symp. on Logic in Computer Science, pp. 255–264. IEEE press, Los Alamitos (2006)
Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Proc. 16th ACM Symp. on Principles of Programming Languages, pp. 179–190 (1989)
Rabin, M.: Decidability of second order theories and automata on infinite trees. Transaction of the AMS 141, 1–35 (1969)
Ravi, K., Bloem, R., Somenzi, F.: A comparative study of symbolic algorithms for the computation of fair cycles. In: Johnson, S.D., Hunt Jr., W.A. (eds.) FMCAD 2000. LNCS, vol. 1954, pp. 143–160. Springer, Heidelberg (2000)
Safra, S.: On the complexity of ω-automata. In: Proc. 29th IEEE Symp. on Foundations of Computer Science, pp. 319–327 (1988)
Safra, S., Vardi, M.: On ω-automata and temporal logic. In: Proc. 21st ACM Symp. on Theory of Computing, pp. 127–137 (1989)
Street, R., Emerson, E.: An elementary decision procedure for the μ-calculus. In: Paredaens, J. (ed.) ICALP 1984. LNCS, vol. 172, pp. 465–472. Springer, Heidelberg (1984)
Vardi, M., Wolper, P.: Automata-theoretic techniques for modal logics of programs. Journal of Computer and Systems Science 32, 182–221 (1986)
Vardi, M., Wolper, P.: Reasoning about infinite computations. Information and Computation 115, 1–37 (1994)
Wolper, P., Vardi, M., Sistla, A.: Reasoning about infinite computation paths. In: Proc. 24th IEEE Symp. on Foundations of Computer Science, pp. 185–194 (1983)
Yan, Q.: Lower bounds for complementation of ω-automata via the full automata technique. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 589–600. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Boker, U., Kupferman, O. (2010). The Quest for a Tight Translation of Büchi to co-Büchi Automata. In: Blass, A., Dershowitz, N., Reisig, W. (eds) Fields of Logic and Computation. Lecture Notes in Computer Science, vol 6300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15025-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-15025-8_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15024-1
Online ISBN: 978-3-642-15025-8
eBook Packages: Computer ScienceComputer Science (R0)