Skip to main content
SpringerLink
Log in

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

  • Conference paper
Implementation and Application of Automata (CIAA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3845))

Included in the following conference series:

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Thomas, W.: Languages, automata, and logic. Handbook of formal languages 3, 389–455 (1997)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  3. de Alfaro, L.: Formal Verification of Probabilistic Systems. PhD thesis, Stanford University, Department of Computer Science (1997)

    Google Scholar 

  4. Baier, C., Kwiatkowska, M.: Model checking for a probabilistic branching time logic with fairness. Distributed Computing 11, 125–155 (1998)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Safra, S.: Complexity of Automata on Infinite Objects. PhD thesis, The Weizmann Institue of Science, Rehovot, Israel (1989)

    Google Scholar 

  8. Michel, M.: Complementation is more difficult with automata on infinite words. Technical report, CNET Paris (1988)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Etessami, K., Holzmann, G.J.: Optimizing Büchi automata. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 153–167. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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. Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  17. Klein, J.: Linear time logic and deterministic omega-automata. Diploma thesis, Universität Bonn, Institut für Informatik (2005)

    Google Scholar 

  18. Paige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM Journal on Computing 16, 973–989 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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

    Article  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  32. Löding, C.: Efficient minimization of deterministic weak omega-automata. Information Processing Letters 79, 105–109 (2001)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik I, Universität Bonn, Römerstrasse 164, 53117, Bonn, Germany

    Joachim Klein & Christel Baier

Authors
  1. Joachim Klein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christel Baier
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Sophia Antipolis, Laboratoire I3S, Les Algorithmes - bât. Euclide B, Université de Nice, 2000, route des lucioles, BP 121, 06903, Sophia Antipolis - Cedex, France

    Jacques Farré

  2. Sophia Antipolis, Ecole Polytechnique, Université de Nice, 930, route des colles, BP 145, 06903, Sophia Antipolis - Cedex, France

    Igor Litovsky

  3. Laboratoire I3S, Université de Nice, Sophia Antipolis & CNRS, France

    Sylvain Schmitz

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Klein, J., Baier, C. (2006). Experiments with Deterministic ω-Automata for Formulas of Linear Temporal Logic. In: Farré, J., Litovsky, I., Schmitz, S. (eds) Implementation and Application of Automata. CIAA 2005. Lecture Notes in Computer Science, vol 3845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11605157_17

Download citation

  • DOI: https://doi.org/10.1007/11605157_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31023-5

  • Online ISBN: 978-3-540-33097-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation