Saturation-Based Incremental LTL Model Checking with Inductive Proofs

  • Vince Molnár
  • Dániel Darvas
  • András Vörös
  • Tamás Bartha
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9035)

Abstract

Efficient symbolic and explicit model checking approaches have been developed for the verification of linear time temporal properties. Nowadays, advances resulted in the combination of on-the-fly search with symbolic encoding in a hybrid solution providing many results by now. In this work, we propose a new hybrid approach that leverages the so-called saturation algorithm both as an iteration strategy during the state space generation and in a new incremental fixed-point computation algorithm to compute strongly connected components (SCCs). In addition, our solution works on-the-fly during state space traversal and exploits the decomposition of the model as an abstraction to inductively prove the absence of SCCs with cheap explicit runs on the components. When a proof cannot be shown, the incremental symbolic fixed-point algorithm will find the SCC, if one exists. Evaluation on the models of the Model Checking Contest shows that our approach outperforms similar algorithms for concurrent systems.

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References

  1. 1.
    Biere, A., Zhu, Y., Clarke, E.: Multiple state and single state tableaux for combining local and global model checking. In: Olderog, E.-R., Steffen, B. (eds.) Correct System Design. LNCS, vol. 1710, pp. 163–179. Springer, Heidelberg (1999)Google Scholar
  2. 2.
    Bradley, A.: Understanding IC3. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 1–14. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Cavada, R., Cimatti, A., Dorigatti, M., Mariotti, A., Micheli, A., Mover, S., Griggio, A., Roveri, M., Tonetta, S.: The nuXmv symbolic model checker. Tech. rep., Fondazione Bruno Kessler (2014)Google Scholar
  4. 4.
    Ciardo, G., Lüttgen, G., Siminiceanu, R.: Saturation: an efficient iteration strategy for symbolic state space generation. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 328–342. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Ciardo, G., Marmorstein, R., Siminiceanu, R.: The saturation algorithm for symbolic state-space exploration. Int. J. on Softw. Tools for Technology Transfer 8(1), 4–25 (2006)CrossRefGoogle Scholar
  6. 6.
    Cimatti, A., Clarke, E., Giunchiglia, E., et al.: NuSMV 2: An opensource tool for symbolic model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 359–364. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Claessen, K., Sorensson, N.: A liveness checking algorithm that counts. In: Formal Methods in Computer-Aided Design, 2012, pp. 52–59. IEEE (2012)Google Scholar
  8. 8.
    Courcoubetis, C., Vardi, M., Wolper, P., Yannakakis, M.: Memory efficient algorithms 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
  9. 9.
    Duret-Lutz, A., Poitrenaud, D.: SPOT: An extensible model checking library using transition-based generalized Büchi automata. In: Proc. of the IEEE Int. Symp. on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems, pp. 76–83 (2004)Google Scholar
  10. 10.
    Duret-Lutz, A., Klai, K., Poitrenaud, D., Thierry-Mieg, Y.: Combining explicit and symbolic approaches for better on-the-fly LTL model checking. arXiv:1106.5700 (cs) (2011)Google Scholar
  11. 11.
    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
  12. 12.
    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
  13. 13.
    Sebastiani, R., Tonetta, S., Vardi, M.: 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
  14. 14.
    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
  15. 15.
    Tarjan, R.: Depth first search and linear graph algorithms. SIAM Journal on Computing 1(2), 146–160 (1972)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Wang, C., Bloem, R., Hachtel, G.D., Ravi, K., Somenzi, F.: Compositional SCC analysis for language emptiness. Form. Method. Syst. Des. 28(1), 5–36 (2006)CrossRefMATHGoogle Scholar
  17. 17.
    Zhao, Y., Ciardo, G.: Symbolic CTL model checking of asynchronous systems using constrained saturation. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 368–381. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  18. 18.
    Zhao, Y., Ciardo, G.: Symbolic computation of strongly connected components and fair cycles using saturation. Innov. Syst. Softw. Eng. 7(2), 141–150 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Vince Molnár
    • 1
  • Dániel Darvas
    • 1
  • András Vörös
    • 1
  • Tamás Bartha
    • 2
  1. 1.Budapest University of Technology and EconomicsBudapestHungary
  2. 2.Institute for Computer Science and ControlHungarian Academy of SciencesBudapestHungary

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