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State of Büchi Complementation

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Implementation and Application of Automata (CIAA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6482))

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Abstract

Büchi complementation has been studied for five decades since the formalism was introduced in 1960. Known complementation constructions can be classified into Ramsey-based, determinization-based, rank-based, and slice-based approaches. For the performance of these approaches, there have been several complexity analyses but very few experimental results. What especially lacks is a comparative experiment on all the four approaches to see how they perform in practice. In this paper, we review the state of Büchi complementation, propose several optimization heuristics, and perform comparative experimentation on the four approaches. The experimental results show that the determinization-based Safra-Piterman construction outperforms the other three and our heuristics substantially improve the Safra-Piterman construction and the slice-based construction.

Work supported in part by the National Science Council, Taiwan (R.O.C.) under grant NSC97-2221-E-002-074-MY3, by NSF grants CCF-0613889, ANI-0216467, CCF-0728882, and OISE-0913807, by BSF grant 9800096, and by gift from Intel.

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References

  1. Abdulla, P.A., Chen, Y.-F., Holík, L., Mayr, R., Vojnar, T.: When simulation meets antichains. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 158–174. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  2. Althoff, C.S., Thomas, W., Wallmeier, N.: Observations on determinization of Büchi automata. Theoretical Computer Science 363(2), 224–233 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Büchi, J.R.: On a decision method in restricted second order arithmetic. In: Proceedings of the International Congress on Logic, Method, and Philosophy of Science 1960, pp. 1–12. Stanford University Press, Stanford (1962)

    Google Scholar 

  4. Doyen, L., Raskin, J.-F.: Antichains for the automata-based approach to model-checking. Logical Methods in Computer Science 5(1:5), 1–20 (2009)

    MathSciNet  MATH  Google Scholar 

  5. Fogarty, S., Vardi, M.Y.: Büchi complementation and size-change termination. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 16–30. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. 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)

    Chapter  Google Scholar 

  7. Friedgut, E., Kupferman, O., Vardi, M.Y.: Büchi complementation made tighter. International Journal of Foundations of Computer Science 17(4), 851–868 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  9. Gurumurthy, S., Kupferman, O., Somenzi, F., Vardi, M.Y.: On complementing nondeterministic Büchi automata. In: Geist, D., Tronci, E. (eds.) CHARME 2003. LNCS, vol. 2860, pp. 96–110. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. 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)

    Chapter  Google Scholar 

  11. Karmarkar, H., Chakraborty, S.: On minimal odd rankings for Büchi complementation. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 228–243. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  12. King, V., Kupferman, O., Vardi, M.Y.: On the complexity of parity word automata. In: Honsell, F., Miculan, M. (eds.) FOSSACS 2001. LNCS, vol. 2030, pp. 276–286. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  13. Klarlund, N.: Progress measures for complementation of omega-automata with applications to temporal logic. In: FOCS, pp. 358–367. IEEE, Los Alamitos (1991)

    Google Scholar 

  14. Klein, J., Baier, C.: Experiments with deterministic ω-automata for formulas of linear temporal logic. Theoretical Computer Science 363(2), 182–195 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kupferman, O., Vardi, M.Y.: Weak alternating automata are not that weak. ACM Transactions on Computational Logic 2(3), 408–429 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kupferman, O., Vardi, M.Y.: Safraless decision procedures. In: FOCS, pp. 531–540. IEEE Computer Society, Los Alamitos (2005)

    Google Scholar 

  17. Michel, M.: Complementation is more difficult with automata on infinite words. Manuscript CNET, Paris (1988)

    Google Scholar 

  18. Muller, D.E., Schupp, P.E.: Simulating alternating tree automata by nondeterministic automata: New results and new proofs of the theorems of Rabin, McNaughton and Safra. Theoretical Computer Science 141(1&2), 69–107 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  19. Piterman, N.: From nondeterministic Büchi and Streett automata to deterministic parity automata. Logical Methods in Computer Science 3(3:5), 1–21 (2007)

    MathSciNet  MATH  Google Scholar 

  20. Safra, S.: On the complexity of ω-automata. In: FOCS, pp. 319–327. IEEE, Los Alamitos (1988)

    Google Scholar 

  21. Schewe, S.: Büchi complementation made tight. In: STACS. LIPIcs, vol. 3, pp. 661–672. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2009)

    Google Scholar 

  22. Sistla, A.P., Vardi, M.Y., Wolper, P.: The complementation problem for Büchi automata with appplications to temporal logic. TCS 49, 217–237 (1987)

    Article  MATH  Google Scholar 

  23. Somenzi, F., Bloem, R.: Efficient Büchi automata from LTL formulae. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 248–263. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  24. Thomas, W.: Complementation of Büchi automata revisited. In: Jewels are Forever, pp. 109–120. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  25. Tsai, M.-H., Fogarty, S., Vardi, M.Y., Tsay, Y.-K.: State of Büchi complementation (full version), http://goal.im.ntu.edu.tw

  26. Tsay, Y.-K., Chen, Y.-F., Tsai, M.-H., Chan, W.-C., Luo, C.-J.: GOAL extended: Towards a research tool for omega automata and temporal logic. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 346–350. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  27. Vardi, M.Y.: An automata-theoretic approach to linear temporal logic. In: Moller, F., Birtwistle, G. (eds.) Logics for Concurrency. LNCS, vol. 1043, pp. 238–266. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  28. Vardi, M.Y.: Automata-theoretic model checking revisited. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 137–150. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  29. Vardi, M.Y.: The Büchi complementation saga. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, pp. 12–22. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  30. Vardi, M.Y., Wilke, T.: Automata: from logics to algorithms. In: Logic and Automata: History and Perspective. Texts in Logic and Games, vol. 2, pp. 629–736. Amsterdam University Press, Amsterdam (2007)

    Google Scholar 

  31. Yan, Q.: Lower bounds for complementation of omega-automata via the full automata technique. Logical Methods in Computer Science 4(1:5), 1–20 (2008)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. National Taiwan University, Taiwan

    Ming-Hsien Tsai & Yih-Kuen Tsay

  2. Rice University, USA

    Seth Fogarty & Moshe Y. Vardi

Authors
  1. Ming-Hsien Tsai
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  2. Seth Fogarty
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  3. Moshe Y. Vardi
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  4. Yih-Kuen Tsay
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Manitoba, R3T 2N2, Winnipeg, MB, Canada

    Michael Domaratzki

  2. School of Computing, Queen’s University, K7L 3N6, Kingston, Ontario, Canada

    Kai Salomaa

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Tsai, MH., Fogarty, S., Vardi, M.Y., Tsay, YK. (2011). State of Büchi Complementation. In: Domaratzki, M., Salomaa, K. (eds) Implementation and Application of Automata. CIAA 2010. Lecture Notes in Computer Science, vol 6482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18098-9_28

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  • DOI: https://doi.org/10.1007/978-3-642-18098-9_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18097-2

  • Online ISBN: 978-3-642-18098-9

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