Advertisement

Self-Loop Aggregation Product — A New Hybrid Approach to On-the-Fly LTL Model Checking

  • Alexandre Duret-Lutz
  • Kais Klai
  • Denis Poitrenaud
  • Yann Thierry-Mieg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6996)

Abstract

We present the Self-Loop Aggregation Product (SLAP), a new hybrid technique that replaces the synchronized product used in the automata-theoretic approach for LTL model checking. The proposed product is an explicit graph of aggregates (symbolic sets of states) that can be interpreted as a Büchi automaton. The criterion used by SLAP to aggregate states from the Kripke structure is based on the analysis of self-loops that occur in the Büchi automaton expressing the property to verify. Our hybrid approach allows on the one hand to use classical emptiness-check algorithms and build the graph on-the-fly, and on the other hand, to have a compact encoding of the state space thanks to the symbolic representation of the aggregates. Our experiments show that this technique often outperforms other existing (hybrid or fully symbolic) approaches.

Keywords

Model Check Linear Temporal Logic Atomic Proposition Acceptance Condition Boolean Formula 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baarir, S., Duret-Lutz, A.: Emptiness check of powerset Büchi automata. In: Proc. of ACSD 2007, pp. 41–50. IEEE Computer Society, Los Alamitos (2007)Google Scholar
  2. 2.
    Biere, A., Clarke, E.M., Zhu, Y.: Multiple state and single state tableaux for combining local and global model checking. In: Olderog, E.-R., Steffen, B. (eds.) CSD 1999. LNCS, vol. 1710, pp. 163–179. Springer, Heidelberg (1999)Google Scholar
  3. 3.
    Ciardo, G., Marmorstein, R., Siminiceanu, R.: Saturation unbound. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 379–393. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Courcoubetis, C., Vardi, M.Y., Wolper, P., Yannakakis, M.: Memory-efficient algorithm for the verification of temporal properties. In: Clarke, E., Kurshan, R.P. (eds.) CAV 1990. LNCS, vol. 531, pp. 233–242. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  5. 5.
    Couvreur, J.-M., Duret-Lutz, A., Poitrenaud, D.: On-the-fly emptiness checks for generalized büchi automata. In: Godefroid, P. (ed.) SPIN 2005. LNCS, vol. 3639, pp. 169–184. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Duret-Lutz, A., Klai, K., Poitrenaud, D., Thierry-Mieg, Y.: Combining explicit and symbolic approaches for better on-the-fly LTL model checking. Technical Report 1106.5700, arXiv (June 2011); Extended version of the present paper, presenting two new techniques instead of one, http://arxiv.org/abs/1106.5700
  7. 7.
    Duret-Lutz, A., Poitrenaud, D.: Spot: an extensible model checking library using transition-based generalized Büchi automata. In: Proc. of MASCOTS 2004, pp. 76–83. IEEE Computer Society Press, Los Alamitos (2004)Google Scholar
  8. 8.
    Etessami, K.: Stutter-invariant languages, ω-automata, and temporal logic. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 236–248. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  9. 9.
    Fisler, K., Fraer, R., Kamhi, G., Vardi, M.Y., Yang, Z.: Is there a best symbolic cycle-detection algorithm? In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 420–434. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Haddad, S., Ilié, J.-M., Klai, K.: Design and evaluation of a symbolic and abstraction-based model checker. In: Wang, F. (ed.) ATVA 2004. LNCS, vol. 3299, pp. 196–210. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Hamez, A., Thierry-Mieg, Y., Kordon, F.: Hierarchical set decision diagrams and automatic saturation. In: van Hee, K.M., Valk, R. (eds.) PETRI NETS 2008. LNCS, vol. 5062, pp. 211–230. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Hansen, H., Penczek, W., Valmari, A.: Stuttering-insensitive automata for on-the-fly detection of livelock properties. In: Proc. of FMICS 2002. Electronic Notes in Theoretical Computer Science, vol. 66(2). Elsevier, Amsterdam (2002)Google Scholar
  13. 13.
    Kaivola, R., Valmari, A.: The weakest compositional semantic equivalence preserving nexttime-less linear temporal logic. In: Cleaveland, W.R. (ed.) CONCUR 1992. LNCS, vol. 630, pp. 207–221. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  14. 14.
    Kesten, Y., Pnueli, A., Raviv, L.-o.: Algorithmic verification of linear temporal logic specifications. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 1–16. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  15. 15.
    Klai, K., Poitrenaud, D.: MC-SOG: An LTL model checker based on symbolic observation graphs. In: van Hee, K.M., Valk, R. (eds.) PETRI NETS 2008. LNCS, vol. 5062, pp. 288–306. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Rozier, K.Y., Vardi, M.Y.: LTL satisfiability checking. In: Bošnački, D., Edelkamp, S. (eds.) SPIN 2007. LNCS, vol. 4595, pp. 149–167. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  17. 17.
    Sebastiani, R., Tonetta, S., Vardi, M.Y.: Symbolic systems, explicit properties: On hybrid approaches for LTL symbolic model checking. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 350–363. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Somenzi, F., Ravi, K., Bloem, R.: Analysis of symbolic SCC hull algorithms. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 88–105. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  19. 19.
    Thierry-Mieg, Y., Poitrenaud, D., Hamez, A., Kordon, F.: Hierarchical set decision diagrams and regular models. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 1–15. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  20. 20.
    Vardi, M.Y.: An automata-theoretic approach to linear temporal logic. In: Moller, F., Birtwistle, G. (eds.) Logics for Concurrency. LNCS, vol. 1043, pp. 238–266. Springer, Heidelberg (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Alexandre Duret-Lutz
    • 1
  • Kais Klai
    • 2
  • Denis Poitrenaud
    • 3
  • Yann Thierry-Mieg
    • 3
  1. 1.LRDE, EPITA, Kremlin-BicêtreFrance
  2. 2.LIPN, Université Paris-NordVilletaneuseFrance
  3. 3.LIP6/MoVe, Université Pierre & Marie CurieParisFrance

Personalised recommendations