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Model-Checking Bounded Multi-Pushdown Systems

  • Kshitij Bansal
  • Stéphane Demri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7913)

Abstract

We provide complexity characterizations of model checking multi-pushdown systems. We consider three standard notions for boundedness: context boundedness, phase boundedness and stack ordering. The logical formalism is a linear-time temporal logic extending well-known logic CaRet but dedicated to multi-pushdown systems in which abstract operators are parameterized by stacks. We show that the problem is ExpTime-complete for context-bounded runs and unary encoding of the number of context switches; we also prove that the problem is 2ExpTime-complete for phase-bounded runs and unary encoding of the number of phase switches. In both cases, the value k is given as an input, which makes a substantial difference in the complexity.

Keywords

Model Check Global State Context Switch Multithreaded Program Regularity Constraint 
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.

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References

  1. 1.
    Alur, R., Etessami, K., Madhusudan, P.: A temporal logic of nested calls and returns. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 467–481. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Atig, M.: Global model checking of ordered multi-pushdown systems. In: FST&TCS 2010. LIPICS, pp. 216–227 (2010)Google Scholar
  3. 3.
    Atig, M.F., Bollig, B., Habermehl, P.: Emptiness of multi-pushdown automata is 2ETIME-complete. In: Ito, M., Toyama, M. (eds.) DLT 2008. LNCS, vol. 5257, pp. 121–133. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Atig, M.F., Bouajjani, A., Narayan Kumar, K., Saivasan, P.: Linear-time model-checking for multithreaded programs under scope-bounding. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 152–166. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  5. 5.
    Bansal, K., Demri, S.: A note on the complexity of model-checking bounded multi-pushdown systems. Technical Report TR2012-949, NYU (December 2012)Google Scholar
  6. 6.
    Bollig, B., Cyriac, A., Gastin, P., Zeitoun, M.: Temporal logics for concurrent recursive programs: Satisfiability and model checking. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 132–144. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Bollig, B., Kuske, D., Mennicke, R.: The complexity of model-checking multi-stack systems (2012) (submitted)Google Scholar
  8. 8.
    Bouajjani, A., Esparza, J., Maler, O.: Reachability analysis of pushdown automata: application to model-checking. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 135–150. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  9. 9.
    Cyriac, A., Gastin, P., Kumar, K.N.: MSO decidability of multi-pushdown systems via split-width. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 547–561. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. 10.
    Esparza, J., Ganty, P.: Complexity of pattern-based verification for multithreaded programs. In: POPL 2011, pp. 499–510. ACM (2011)Google Scholar
  11. 11.
    Esparza, J., Kučera, A., Schwoon, S.: Model-checking LTL with regular valuations for pushdown systems. In: Kobayashi, N., Babu, C. S. (eds.) TACS 2001. LNCS, vol. 2215, pp. 316–339. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    La Torre, S., Madhusudan, P., Parlato, G.: A robust class of context-sensitive languages. In: LICS 2007, pp. 161–170. IEEE (2007)Google Scholar
  13. 13.
    La Torre, S., Napoli, M.: Reachability of multistack pushdown systems with scope-bounded matching relations. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 203–218. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    La Torre, S., Napoli, M.: A temporal logic for multi-threaded programs. In: Baeten, J.C.M., Ball, T., de Boer, F.S. (eds.) TCS 2012. LNCS, vol. 7604, pp. 225–239. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  15. 15.
    La Torre, S., Parlato, G.: Scope-bounded multistack pushdown systems: fixed-point, sequentialization and tree-width. In: FSTTCS 2012. LIPICS, pp. 173–184 (2012)Google Scholar
  16. 16.
    Madhusudan, P., Parlato, G.: The tree width of auxiliary storage. In: POPL 2011, pp. 283–294. ACM (2011)Google Scholar
  17. 17.
    Qadeer, S., Rehof, J.: Context-bounded model checking of concurrent software. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 93–107. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Schwoon, S.: Model-checking pushdown systems. PhD thesis, TUM (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Kshitij Bansal
    • 1
  • Stéphane Demri
    • 1
    • 2
  1. 1.New York UniversityUSA
  2. 2.LSV, CNRSFrance

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