Constructing Büchi Automata from Linear Temporal Logic Using Simulation Relations for Alternating Büchi Automata

  • Carsten Fritz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2759)

Abstract

We present a new procedure for the translation of propositional linear-time temporal logic (LTL) formulas to equivalent nondeterministic Büchi automata. Our procedure is based on simulation relations for alternating Büchi automata. Whereas most of the procedures that have been described in the past compute simulation relations in the last step of the translation (after a nondeterministic Büchi automaton has already been constructed), our procedure computes simulation relations for alternating Büchi automata in an early stage and uses them in an on-the- fly fashion. This decreases the time and space consumption without sacrificing the potential of simulation relations.

We present experimental results that demonstrate the advantages of our approach: Our procedure is faster than TMP but produces, on the average, automata of about the same size; LTL2BA is faster than our procedure but produces larger automata.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AHKV98]
    R. Alur, Th.A. Henzinger, O. Kupferman, and M.Y. Vardi. Alternating refinement relations. In D. Sangiorgi and R. de Simone, eds., 9th Int. Conf. on Concurrency Theory (CONCUR’ 98), vol. 1466 of LNCS, pp. 163–178, 1998.CrossRefGoogle Scholar
  2. [AS03]
    A. Arnold and L. Santocanale. Ambigious classes in the games μ-calculus hierarchy. In A. D. Gordon, ed., 6th Int. Conf. on Foundations of Software Science and Computational Structures (FOSSACS’ 03), vol. 2620 of LNCS, pp. 70–86, 2003.CrossRefGoogle Scholar
  3. [ATT]
    AT & T Labs-Research. Graphviz. http://www.research.att.com/sw/tools/graphviz/.
  4. [Blo]
    R. Bloem. Wring: an LTL to Buechi translator. URL: http://vlsi.colorado.edu/~rbloem/wring.html.
  5. [DHW91]
    D. L. Dill, A. J. Hu, and H. Wong-Toi. Checking for language inclusion using simulation preorders. In Kim Guldstrand Larsen and Arne Skou, eds., Computer Aided Verification, 3rd Int. Workshop, CAV’ 91, vol. 575 of LNCS, pp. 255–265, 1991.Google Scholar
  6. [EH00]
    K. Etessami and G. Holzmann. Optimizing Büchi automata. In C. Palamidessi, ed., 11th Int. Conf. on Concurrency Theory (CONCUR 2000), vol. 1877 of LNCS, pp. 153–167, 2000.CrossRefGoogle Scholar
  7. [ESW01]
    K. Etessami, R. Schuller, and Th. Wilke. Fair simulation relations, parity games, and state space reduction for Büchi automata. In F. Orejas, P.G. Spirakis, and J. van Leeuwen, eds., ICALP, volume 2076 of LNCS, pp. 694–707. Springer-Verlag, 2001.Google Scholar
  8. [Ete]
    K. Etessami. Temporal massage parlor. http://www1.bell-labs.com/project/TMP/.
  9. [Fri]
  10. [FT]
  11. [FW02a]
    C. Fritz and Th. Wilke. Simulation relations for alternating Büchi automata. Tech. Rep. 2019, Institut für Informatik, Kiel University, July 2002. Extended version. Available at http://www.ti.informatik.uni-kiel.de/~fritz/TechRep2019ext.ps.
  12. [FW02b]
    C. Fritz and Th. Wilke. State space reductions for alternating Büchi automata: Quotienting by simulation equivalences. In M. Agrawal and A. Seth, eds., 22nd Conf. on Foundations of Software Technology and Theoretical Computer Science, vol. 2556 of LNCS, pp. 157–168, 2002.Google Scholar
  13. [GBS02]
    S. Gurumurthy, R. Bloem, and F. Somenzi. Fair simulation minimization. In E. Brinksma and K. Guldstrand Larsen, eds., Computer Aided Verification. 14th International Conference, CAV 2002, vol. 2404 of LNCS, pp. 610–623, 2002.CrossRefGoogle Scholar
  14. [GJ79]
    M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Co., San Francisco, 1979.MATHGoogle Scholar
  15. [GO01]
    P. Gastin and D. Oddoux. Fast LTL to Büchi automata translation. In G. Berry, H. Comon, and A. Finkel, eds., Computer Aided Verification. 13th International Conference, CAV 2001, vol. 2102 of LNCS, pp. 53–65. Springer-Verlag, 2001.Google Scholar
  16. [GPVW95]
    R. Gerth, D. Peled, M.Y. Vardi, and P. Wolper. Simple on-the-fly automatic verification of linear temporal logic. In Proc. of the 15th Workshop on Protocol Specification, Testing, and Verification, pp. 3–18, Warsaw, Poland, June 1995. Chapman Hall.Google Scholar
  17. [HHK95]
    M. Henzinger Rauch, Th.A. Henzinger, and P.W. Kopke. Computing simulations on finite and infinite graphs. In 36th Ann. Symp. on Foundations of Computer Science (FOCS’ 95), pp. 453–462, 1995.Google Scholar
  18. [HKR97]
    Th.A. Henzinger, O. Kupferman, and S.K. Rajamani. Fair simulation. In CONCUR’ 97, vol. 1243 of LNCS, pp. 273–287, 1997.Google Scholar
  19. [Hol]
    G. J. Holzmann. The SPIN homepage. http://netlib.bell-labs.com/netlib/spin/whatispin.html.
  20. [HR00]
    Th.A. Henzinger and S.K. Rajamani. Fair bisimulation. In S. Graf and M. Schwartzbach, eds., TACAS’ 00: Tools and Algorithms for the Construction and Analysis of Systems, vol. 1785 of LNCS, pp. 299–314. Springer-Verlag, 2000.CrossRefGoogle Scholar
  21. [Jur00]
    M. Jurdzi’mski. Small progress measures for solving parity games. In H. Reichel and S. Tison, eds., STACS 2000, 17th Ann. Symp. on Theoretical Aspects of Computer Science, vol. 1770 of LNCS, pp. 290–301, 2000. Springer-Verlag.Google Scholar
  22. [MH84]
    S. Miyano and T. Hayashi. Alternating finite automata on ω-words. Theoretical Computer Science, 32:321–330, 1984.MATHCrossRefMathSciNetGoogle Scholar
  23. [Mil71]
    R. Milner. An algebraic definition of simulation between programs. In D. C. Cooper, editor, Proc. of the 2nd Int. Joint Conf. on Artificial Intelligence, pp. 481–489, London, UK, September 1971. William Kaufmann. ISBN 0-934613-34-6.Google Scholar
  24. [Mil80]
    R. Milner. A Calculus of Communicating Systems, vol. 92 of LNCS. Springer-Verlag, 1980.MATHGoogle Scholar
  25. [MP92]
    Z. Manna and A. Pnueli. The Temporal Logic of Reactive and Concurrent Systems. Springer-Verlag, 1992.Google Scholar
  26. [MSS86]
    D.E. Muller, A. Saoudi, and P.E. Schupp. Alternating automata, the weak monadic theory of the tree and its complexity. In Proc. 13th Int. Coll. on Automata, Languages, and Programming (ICALP’ 86), vol. 226 of LNCS, 1986.Google Scholar
  27. [Odd]
  28. [Par81]
    D. M. R. Park. Concurrency and automata on infinite sequences. In P. Deussen, ed., 5th GI Conference, vol. 104 of LNCS, pp. 167–183, 1981.Google Scholar
  29. [SB00]
    F. Somenzi and R. Bloem. Efficient Büchi automata from LTL formulae. In E. Allen Emerson and A. Prasad Sistla, eds., Computer Aided Verification, 12th International Conference (CAV 2000), vol. 1855 of LNCS, pp. 248–263, 2000.CrossRefGoogle Scholar
  30. [TH02]
    H. Tauriainen and K. Heljanko. Testing LTL formula translation into Büchi automata. Int. Journal on Software Tools for Technology Transfer, 4(1):57–70, 2002.CrossRefGoogle Scholar
  31. [Var96]
    M.Y. Vardi. An automata-theoretic approach to linear temporal logic. In Logics for Concurrency: Structure versus Automata, vol. 1043 of LNCS, pp. 238–266, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Carsten Fritz
    • 1
  1. 1.Institut für Informatik und Praktische MathematikCAU KielGermany

Personalised recommendations