Experiments with Deterministic ω-Automata for Formulas of Linear Temporal Logic

  • Joachim Klein
  • Christel Baier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3845)


This paper addresses the problem of generating deterministic ω-automata for formulas of linear temporal logic, which can be solved by applying well-known algorithms to construct a nondeterministic Büchi automaton for the given formula on which we then apply a determinization algorithm. We study here in detail Safra’s determinization algorithm, present several heuristics that attempt to decrease the size of the resulting automata and report on experimental results.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Thomas, W.: Languages, automata, and logic. Handbook of formal languages 3, 389–455 (1997)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  3. 3.
    de Alfaro, L.: Formal Verification of Probabilistic Systems. PhD thesis, Stanford University, Department of Computer Science (1997)Google Scholar
  4. 4.
    Baier, C., Kwiatkowska, M.: Model checking for a probabilistic branching time logic with fairness. Distributed Computing 11, 125–155 (1998)CrossRefGoogle Scholar
  5. 5.
    Vardi, M.: Probabilistic linear-time model checking: An overview of the automata-theoretic approach. In: Katoen, J.-P. (ed.) AMAST-ARTS 1999, ARTS 1999, and AMAST-WS 1999. LNCS, vol. 1601, pp. 265–276. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Safra, S.: On the complexity of ω-automata. In: Proc. 29th Annual Symposium on Foundations of Computer Science (FOCS), pp. 319–327. IEEE Computer Society Press, Los Alamitos (1988)Google Scholar
  7. 7.
    Safra, S.: Complexity of Automata on Infinite Objects. PhD thesis, The Weizmann Institue of Science, Rehovot, Israel (1989)Google Scholar
  8. 8.
    Michel, M.: Complementation is more difficult with automata on infinite words. Technical report, CNET Paris (1988)Google Scholar
  9. 9.
    Löding, C.: Optimal bounds for the transformation of omega-automata. In: Pandu Rangan, C., Raman, V., Ramanujam, R. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 97–109. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  10. 10.
    Kupferman, O., Vardi, M.Y.: Freedom, weakness, and determinism: From linear-time to branching-time. In: Proc. 13th IEEE Symposium on Logic in Computer Science, pp. 81–92 (1998)Google Scholar
  11. 11.
    Etessami, K., Holzmann, G.J.: Optimizing Büchi automata. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 153–167. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    Dwyer, M.B., Avrunin, G.S., Corbett, J.C.: Patterns in property specifications for finite-state verification. In: ICSE, pp. 411–420 (1999)Google Scholar
  14. 14.
    Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. B: Formal Models and Semantics, pp. 995–1072. Elsevier Science Publishers, Amsterdam (1990)Google Scholar
  15. 15.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)Google Scholar
  16. 16.
    Etessami, K., Wilke, T., Schuller, R.A.: Fair simulation relations, parity games, and state space reduction for Büchi automata. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 694–707. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  17. 17.
    Klein, J.: Linear time logic and deterministic omega-automata. Diploma thesis, Universität Bonn, Institut für Informatik (2005)Google Scholar
  18. 18.
    Paige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM Journal on Computing 16, 973–989 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Kupferman, O., Vardi, M.Y.: Model checking of safety properties. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, Springer, Heidelberg (1999)CrossRefGoogle Scholar
  20. 20.
    Latvala, T.: On model checking safety properties. Research Report A76, Helsinki University of Technology, Laboratory for Theoretical Computer Science, Espoo, Finland (2002)Google Scholar
  21. 21.
    Tasiran, S., Hojati, R., Brayton, R.K.: Language containment of non-deterministic ω-automata. In: Camurati, P.E., Eveking, H. (eds.) CHARME 1995. LNCS, vol. 987, pp. 261–277. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  22. 22.
    Tauriainen, H.: Automated testing of Büchi automata translators for linear temporal logic. Research report, Helsinki University of Technology, Laboratory for Theoretical Computer Science (2000)Google Scholar
  23. 23.
    Sebastiani, R., Tonetta, S.: More Deterministic vs. ”Smaller” Büchi Automata for Efficient LTL Model Checking. In: Geist, D., Tronci, E. (eds.) CHARME 2003. LNCS, vol. 2860, pp. 126–140. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  24. 24.
    Holzmann, G.J.: The Model Checker Spin. IEEE Trans. on Software Engineering 23, 279–295 (1997), Special issue on Formal Methods in Software Practice CrossRefGoogle Scholar
  25. 25.
    Gerth, R., Peled, D., Vardi, M.Y., Wolper, P.: Simple on-the-fly automatic verification of linear temporal logic. In: Proc. PSTV 1995. IFIP Conference Proceedings, vol. 38, pp. 3–18. Chapman and Hall, Boca Raton (1995)Google Scholar
  26. 26.
    Fritz, C.: Constructing Büchi automata from linear temporal logic using simulation relations for alternating Büchi automata. In: H. Ibarra, O., Dang, Z. (eds.) CIAA 2003. LNCS, vol. 2759, pp. 35–48. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  27. 27.
    Gastin, P., Oddoux, D.: Fast LTL to Büchi automata translation. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 53–65. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  28. 28.
    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, 69–107 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Althoff, C.S., Thomas, W., Wallmeier, N.: Observations on determinization of Büchi automata. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, Springer, Heidelberg (2006)CrossRefGoogle Scholar
  30. 30.
    Emerson, E.A., Sistla, A.P.: Deciding branching time logic. In: STOC 1984, pp. 14–24. ACM Press, New York (1984)Google Scholar
  31. 31.
    Krishnan, S.C., Puri, A., Brayton, R.K.: Deterministic ω Automata vis-a-vis Deterministic Buchi Automata. In: Du, D.-Z., Zhang, X.-S. (eds.) ISAAC 1994. LNCS, vol. 834, pp. 378–386. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  32. 32.
    Löding, C.: Efficient minimization of deterministic weak omega-automata. Information Processing Letters 79, 105–109 (2001)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Joachim Klein
    • 1
  • Christel Baier
    • 1
  1. 1.Institut für Informatik IUniversität BonnBonnGermany

Personalised recommendations