Improved Ramsey-Based Büchi Complementation

  • Stefan Breuers
  • Christof Löding
  • Jörg Olschewski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7213)


We consider complementing Büchi automata by applying the Ramsey-based approach, which is the original approach already used by Büchi and later improved by Sistla et al. We present several heuristics to reduce the state space of the resulting complement automaton and provide experimental data that shows that our improved construction can compete (in terms of finished complementation tasks) also in practice with alternative constructions like rank-based complementation. Furthermore, we show how our techniques can be used to improve the Ramsey-based complementation such that the asymptotic upper bound for the resulting complement automaton is \(2^{{\mathcal O}(n {\rm log} n)}\) instead of \(2^{{\mathcal O}(n^2)}\).


Complementation Method Greedy Strategy Alternative Construction Total Preorder Loop Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Abdulla, P.A., Chen, Y.-F., Clemente, L., Holík, L., Hong, C.-D., Mayr, R., Vojnar, T.: Advanced Ramsey-based Büchi Automata Inclusion Testing. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011 – Concurrency Theory. LNCS, vol. 6901, pp. 187–202. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. 2.
    Büchi, J.R.: On a decision method in restricted second order arithmetic. In: Logic, Methodology and Philosophy of Science, pp. 1–11. Stanford Univerity Press (1962)Google Scholar
  3. 3.
    Fogarty, S., Kupferman, O., Vardi, M.Y., Wilke, T.: Unifying Büchi complementation constructions. In: CSL (2011)Google Scholar
  4. 4.
    Fogarty, S., Vardi, M.Y.: Efficient Büchi Universality Checking. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 205–220. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Friedgut, E., Kupferman, O., Vardi, M.Y.: Büchi complementation made tighter. International Journal of Foundations of Computer Science 17(4), 851–868 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Kähler, D., Wilke, T.: Complementation, Disambiguation, and Determinization of Büchi Automata Unified. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 724–735. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Klarlund, N.: Progress measures for complementation of ω-automata with applications to temporal logic. In: FOCS, pp. 358–367. IEEE Computer Society (1991)Google Scholar
  8. 8.
    Michel, M.: Complementation is more difficult with automata on infinite words. Technical report, CNET, Paris (1988)Google Scholar
  9. 9.
    Piterman, N.: From nondeterministic Büchi and Streett automata to deterministic parity automata. Logical Methods in Computer Science 3(3) (2007)Google Scholar
  10. 10.
    Ramsey, F.P.: On a problem of formal logic. Proceedings of the London Mathematical Society 2(1), 264 (1930)CrossRefGoogle Scholar
  11. 11.
    Safra, S.: On the complexity of ω-automata. In: FOCS, pp. 319–327. IEEE (1988)Google Scholar
  12. 12.
    Schewe, S.: Büchi complementation made tight. In: STACS. LIPIcs, vol. 3, pp. 661–672. Schloss Dagstuhl (2009)Google Scholar
  13. 13.
    Sistla, A.P., Vardi, M.Y., Wolper, P.: The complementation problem for Büchi automata with applications to temporal logic. Theoretical Computer Science 49, 217–237 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Thomas, W.: Automata on infinite objects. In: Handbook of Theoretical Computer Science. Formal Models and Semantics, vol. B, pp. 133–192. Elsevier Science Publishers, Amsterdam (1990)Google Scholar
  15. 15.
    Tsai, M.-H., Fogarty, S., Vardi, M.Y., Tsay, Y.-K.: State of Büchi Complementation. In: Domaratzki, M., Salomaa, K. (eds.) CIAA 2010. LNCS, vol. 6482, pp. 261–271. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  16. 16.
    Yan, Q.: Lower bounds for complementation of ω-automata via the full automata technique. Logical Methods in Computer Science 4(1) (2008)Google Scholar
  17. 17.

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Stefan Breuers
    • 1
  • Christof Löding
    • 1
  • Jörg Olschewski
    • 1
  1. 1.RWTH Aachen UniversityGermany

Personalised recommendations