Multi-core Emptiness Checking of Timed Büchi Automata Using Inclusion Abstraction

  • Alfons Laarman
  • Mads Chr. Olesen
  • Andreas Engelbredt Dalsgaard
  • Kim Guldstrand Larsen
  • Jaco van de Pol
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8044)

Abstract

This paper contributes to the multi-core model checking of timed automata (TA) with respect to liveness properties, by investigating checking of TA Büchi emptiness under the very coarse inclusion abstraction or zone subsumption, an open problem in this field.

We show that in general Büchi emptiness is not preserved under this abstraction, but some other structural properties are preserved. Based on those, we propose a variation of the classical nested depth-first search (ndfs) algorithm that exploits subsumption. In addition, we extend the multi-core cndfs algorithm with subsumption, providing the first parallel LTL model checking algorithm for timed automata.

The algorithms are implemented in LTSmin, and experimental evaluations show the effectiveness and scalability of both contributions: subsumption halves the number of states in the real-world FDDI case study, and the multi-core algorithm yields speedups of up to 40 using 48 cores.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alur, R., Dill, D.L.: A theory of timed automata. TCS 126(2), 183–235 (1994)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Baier, C., Katoen, J.-P.: Principles of Model Checking. The MIT Press (2008)Google Scholar
  3. 3.
    Behrmann, G.: Distributed reachability analysis in timed automata. STTT 7(1), 19–30 (2005)CrossRefGoogle Scholar
  4. 4.
    Behrmann, G., Bouyer, P., Larsen, K.G., Pelánek, R.: Lower and upper bounds in zone based abstractions of timed automata. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 312–326. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Behrmann, G., David, A., Larsen, K.G.: A tutorial on uppaal. In: Bernardo, M., Corradini, F. (eds.) SFM-RT 2004. LNCS, vol. 3185, pp. 200–236. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Bengtsson, J.: Clocks, DBMs and States in Timed Systems. PhD thesis, Uppsala University (2002)Google Scholar
  7. 7.
    Blom, S., van de Pol, J., Weber, M.: lTSmin: Distributed and symbolic reachability. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 354–359. Springer, Heidelberg (2010)Google Scholar
  8. 8.
    Bouajjani, A., Tripakis, S., Yovine, S.: On-the-fly symbolic model checking for real-time systems. In: 18th IEEE RTSS, pp. 25–34. IEEE (1997)Google Scholar
  9. 9.
    Courcoubetis, C., Vardi, M.Y., 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
  10. 10.
    Dalsgaard, A.E., Hansen, R.R., Jørgensen, K.Y., Larsen, K.G., Olesen, M.C., Olsen, P., Srba, J.: opaal: A lattice model checker. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 487–493. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Dalsgaard, A.E., Laarman, A., Larsen, K.G., Olesen, M.C., van de Pol, J.: Multi-core reachability for timed automata. In: Jurdziński, M., Ničković, D. (eds.) FORMATS 2012. LNCS, vol. 7595, pp. 91–106. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  12. 12.
    Daws, C., Tripakis, S.: Model checking of real-time reachability properties using abstractions. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 313–329. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  13. 13.
    Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  14. 14.
    Evangelista, S., Laarman, A., Petrucci, L., van de Pol, J.: Improved multi-core nested depth-first search. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 269–283. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  15. 15.
    Evangelista, S., Petrucci, L., Youcef, S.: Parallel nested depth-first searches for LTL model checking. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 381–396. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  16. 16.
    Holzmann, G.J., Peled, D., Yannakakis, M.: On nested depth-first search. In: The Spin Verification System, 2nd SPIN Workshop, pp. 23–32. AMS (1996)Google Scholar
  17. 17.
    Laarman, A., Langerak, R., van de Pol, J., Weber, M., Wijs, A.: Multi-core nested depth-first search. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 321–335. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  18. 18.
    Laarman, A.W., van de Pol, J.C.: Variations on multi-core nested depth-first search. In: PDMC, vol. 72, pp. 13–28 (2011)Google Scholar
  19. 19.
    Laarman, A.W., van de Pol, J.C., Weber, M.: Boosting multi-core reachability performance with shared hash tables. In: FMCAD. IEEE Computer Society (2010)Google Scholar
  20. 20.
    Laarman, A., van de Pol, J., Weber, M.: Multi-core lTSmin: Marrying modularity and scalability. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 506–511. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  21. 21.
    Laarman, A., van de Pol, J., Weber, M.: Parallel recursive state compression for free. In: Groce, A., Musuvathi, M. (eds.) SPIN Workshops 2011. LNCS, vol. 6823, pp. 38–56. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  22. 22.
    Larsen, K., Pettersson, P., Yi, W.: Uppaal in a nutshell. STTT 1, 134–152 (1997)CrossRefMATHGoogle Scholar
  23. 23.
    Li, G.: Checking timed büchi automata emptiness using LU-abstractions. In: Ouaknine, J., Vaandrager, F.W. (eds.) FORMATS 2009. LNCS, vol. 5813, pp. 228–242. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  24. 24.
    Schwoon, S., Esparza, J.: A note on on-the-fly verification algorithms. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 174–190. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  25. 25.
    Tripakis, S.: Checking timed Büchi automata emptiness on simulation graphs. TOCL 10(3), 15 (2009)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Tripakis, S., Yovine, S., Bouajjani, A.: Checking timed Büchi automata emptiness efficiently. Formal Methods in System Design 26(3), 267–292 (2005)CrossRefMATHGoogle Scholar
  27. 27.
    Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: LICS, pp. 332–344. IEEE (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Alfons Laarman
    • 1
  • Mads Chr. Olesen
    • 2
  • Andreas Engelbredt Dalsgaard
    • 2
  • Kim Guldstrand Larsen
    • 2
  • Jaco van de Pol
    • 1
  1. 1.Formal Methods and ToolsUniversity of TwenteThe Netherlands
  2. 2.Department of Computer ScienceAalborg UniversityDenmark

Personalised recommendations