“More Deterministic” vs. “Smaller” Büchi Automata for Efficient LTL Model Checking

  • Roberto Sebastiani
  • Stefano Tonetta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2860)

Abstract

The standard technique for LTL model checking (\(M \vDash \neg \varphi\)) consists on translating the negation of the LTL specification, ϕ, into a Büchi automaton Aϕ, and then on checking if the product M ×Aϕ has an empty language. The efforts to maximize the efficiency of this process have so far concentrated on developing translation algorithms producing Büchi automata which are “as small as possible”, under the implicit conjecture that this fact should make the final product smaller. In this paper we build on a different conjecture and present an alternative approach in which we generate instead Büchi automata which are “as deterministic as possible”, in the sense that we try to reduce as much as we are able to the presence of non-deterministic decision states in Aϕ. We motivate our choice and present some empirical tests to support this approach.

References

  1. 1.
    Daniele, M., Giunchiglia, F., Vardi, M.: Improved Automata Generation for Linear Time Temporal Logic. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 249–260. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  2. 2.
    Emerson, E.A.: Temporal and Modal Logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. B, pp. 995–1072. Elsevier Science Publisher B.V., Amsterdam (1990)Google Scholar
  3. 3.
    Etessami, K., Holtzmann, G.: Optimizing Büchi Automata. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, p. 153. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    Etessami, K., Schuller, R., Wilke, T.: Fair Simulation Relations, Parity Games, and State Space Reduction for Buechi Automata. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, p. 694. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    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
  6. 6.
    Gerth, R., Peled, D., Vardi, M., Wolper, P.: Simple on-the-fly automatic verification of linear temporal logic. In: Proc. 15th IFIP/WG6.1 Symposium on Protocol Specification, Testing and Verification, Warzaw, Poland, Chapman & Hall, Boca Raton (1995)Google Scholar
  7. 7.
    Giannakopoulou, D., Lerda, F.: From States to Transitions: Improving Translation of LTL Formulae to Büchi Automata. In: Peled, D.A., Vardi, M.Y. (eds.) FORTE 2002. LNCS, vol. 2529, Springer, Heidelberg (2002)Google Scholar
  8. 8.
    Giunchiglia, F., Sebastiani, R.: Building decision procedures for modal logics from propositional decision procedures – the case study of modal K(m). Information and Computation 162(1/2) (October/November 2000)Google Scholar
  9. 9.
    Gurumurty, S., Bloem, R., Somenzi, F.: Fair Simulation Minimization. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, p. 610. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Holtzmann, G.: The Model Checker Spin. IEEE Trans. on Software Engineering 23(5), 279–295 (1997)CrossRefGoogle Scholar
  11. 11.
    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 (June 1998)Google 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, Springer, Heidelberg (2000)CrossRefGoogle Scholar
  13. 13.
    Tauriainen, H.: A Randomized Testbench for Algorithms Translating Linear Temporal Logic Formulae into Büchi Automata. In: Proceedings of the Concurrency, Specification and Programming 1999 Workshop (CS&P 1999), Warsaw University, September 1999, pp. 251–262 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Roberto Sebastiani
    • 1
  • Stefano Tonetta
    • 1
  1. 1.DITUniversità di TrentoPovo, TrentoItaly

Personalised recommendations