Improved Algorithms for the Automata-Based Approach to Model-Checking

  • Laurent Doyen
  • Jean-François Raskin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4424)

Abstract

We propose and evaluate new algorithms to support the automata-based approach to model-checking: algorithms to solve the universality and language inclusion problems for nondeterministic Büchi automata. To obtain those new algorithms, we establish the existence of pre-orders that can be exploited to efficiently evaluate fixed points on the automata defined during the complementation step (that we keep implicit in our approach). We evaluate the performance of our new algorithm to check for universality of Büchi automata experimentally using the random automaton model recently proposed by Tabakov and Vardi. We show that on the difficult instances of this probabilistic model, our algorithm outperforms the standard ones by several orders of magnitude. This work is an extension to the infinite words case of new algorithms for the finite words case that we and co-authors have presented in a recent paper [DDHR06].

Keywords

Maximal Element Improve Algorithm Simulation Relation Emptiness Problem Language Inclusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [BL69]
    Büchi, J.R., Landweber, L.H.: Definability in the monadic second-order theory of successor. J. Symb. Log. 34(2), 166–170 (1969)CrossRefMATHGoogle Scholar
  2. [DDHR06]
    De Wulf, M., et al.: Antichains: A new algorithm for checking universality of finite automata. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 17–30. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. [DR06]
    Doyen, L., Raskin, J.-F.: Improved Algorithms for the Automata-Based Approach to Model-Checking (extended version). Tech. Rep. 76, U.L.B. – Federated Center in Verification (2006), http://www.ulb.ac.be/di/ssd/cfv/publications.html
  4. [EWS05]
    Etessami, K., Wilke, T., Schuller, R.A.: Fair simulation relations, parity games, and state space reduction for büchi automata. SIAM J. Comput. 34(5), 1159–1175 (2005)CrossRefMathSciNetMATHGoogle Scholar
  5. [GKSV03]
    Gurumurthy, S., et al.: On complementing nondeterministic büchi automata. In: Geist, D., Tronci, E. (eds.) CHARME 2003. LNCS, vol. 2860, pp. 96–110. Springer, Heidelberg (2003)Google Scholar
  6. [GO01]
    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)Google Scholar
  7. [KV97]
    Kupferman, O., Vardi, M.Y.: Weak alternating automata are not that weak. In: Proceedings of ISTCS’97, pp. 147–158. IEEE Computer Society Press, Los Alamitos (1997)Google Scholar
  8. [MH84]
    Miyano, S., Hayashi, T.: Alternating finite automata on omega-words. In: CAAP, pp. 195–210 (1984)Google Scholar
  9. [Mic88]
    Michel, M.: Complementation is more difficult with automata on infinite words. In: CNET, Paris (1988)Google Scholar
  10. [RH04]
    Ruys, T.C., Holzmann, G.J.: Advanced spin tutorial. In: Graf, S., Mounier, L. (eds.) SPIN 2004. LNCS, vol. 2989, pp. 304–305. Springer, Heidelberg (2004)Google Scholar
  11. [Saf88]
    Safra, S.: On the complexity of ω-automata. In: Proc. of FOCS: Foundations of Computer Science, pp. 319–327. IEEE Computer Society Press, Los Alamitos (1988)Google Scholar
  12. [SVW87]
    Sistla, A.P., Vardi, M.Y., Wolper, P.: The Complementation Problem for Büchi Automata with Applications to Temporal Logic. Theor. Comput. Sci. 49, 217–237 (1987)CrossRefMathSciNetMATHGoogle Scholar
  13. [Tab06]
    Tabakov, D.: Experimental evaluation of explicit and symbolic approaches to complementation of non-deterministic buechi automata. Talk at “Games and Verification” workshop, Newton Institute for Math. Sciences (July 2006)Google Scholar
  14. [TV05]
    Tabakov, D., Vardi, M.Y.: Experimental evaluation of classical automata constructions. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS (LNAI), vol. 3835, pp. 396–411. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. [VW86]
    Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification (prelim. report). In: LICS, pp. 332–344. IEEE Computer Society Press, Los Alamitos (1986)Google Scholar
  16. [VW94]
    Vardi, M.Y., Wolper, P.: Reasoning about infinite computations. Inf. Comput. 115(1), 1–37 (1994)CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Laurent Doyen
    • 1
  • Jean-François Raskin
    • 2
  1. 1.I&C, Ecole Polytechnique Fédérale de Lausanne (EPFL)Switzerland
  2. 2.CS, Université Libre de Bruxelles (ULB)Belgium

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