Advertisement

Verifying Communicating Multi-pushdown Systems via Split-Width

  • C. Aiswarya
  • Paul Gastin
  • K. Narayan Kumar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8837)

Abstract

Communicating multi-pushdown systems model networks of multi-threaded recursive programs communicating via reliable FIFO channels. We extend the notion of split-width [8] to this setting, improving and simplifying the earlier definition. Split-width, while having the same power of clique-/tree-width, gives a divide-and-conquer technique to prove the bound of a class, thanks to the two basic operations, shuffle and merge, of the split-width algebra. We illustrate this technique on examples. We also obtain simple, uniform and optimal decision procedures for various verification problems parametrised by split-width.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alur, R., Madhusudan, P.: Adding nesting structure to words. Journal of the ACM 56(3), 1–43 (2009)MathSciNetCrossRefGoogle Scholar
  2. 2.
    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
  3. 3.
    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
  4. 4.
    Bollig, B., Kuske, D., Meinecke, I.: Propositional dynamic logic for message-passing systems. Logical Methods in Computer Science 6(3:16) (2010)Google Scholar
  5. 5.
    Breveglieri, L., Cherubini, A., Citrini, C., Crespi-Reghizzi, S.: Multi-pushdown languages and grammars. Int. J. Found. Comput. Sci. 7(3), 253–292 (1996)CrossRefzbMATHGoogle Scholar
  6. 6.
    Courcelle, B.: Special tree-width and the verification of monadic second-order graph properties. In: FSTTCS. LIPIcs, vol. 8, pp. 13–29 (2010)Google Scholar
  7. 7.
    Cyriac, A.: Verification of Communicating Recursive Programs via Split-width. PhD thesis, ENS Cachan (2014), http://www.lsv.ens-cachan.fr/~cyriac/download/Thesis_Aiswarya_Cyriac.pdf
  8. 8.
    Cyriac, A., Gastin, P., Narayan Kumar, K.: 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
  9. 9.
    Cyriac, A., Gastin, P., Narayan Kumar, K.: Verifying Communicating Multi-pushdown Systems. Technical report (January 2014), http://hal.archives-ouvertes.fr/hal-00943690
  10. 10.
    Ganty, P., Majumdar, R., Monmege, B.: Bounded underapproximations. Formal Methods in System Design 40(2), 206–231 (2012)CrossRefzbMATHGoogle Scholar
  11. 11.
    Genest, B., Kuske, D., Muscholl, A.: A Kleene theorem and model checking algorithms for existentially bounded communicating automata. Inf. Comput. 204(6), 920–956 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Göller, S., Lohrey, M., Lutz, C.: PDL with intersection and converse: satisfiability and infinite-state model checking. J. Symb. Log. 74(1), 279–314 (2009)CrossRefzbMATHGoogle Scholar
  13. 13.
    Henriksen, J.G., Mukund, M., Narayan Kumar, K., Sohoni, M.A., Thiagarajan, P.S.: A theory of regular MSC languages. Inf. Comput. 202(1), 1–38 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Henriksen, J.G., Thiagarajan, P.S.: Dynamic linear time temporal logic. Ann. Pure Appl. Logic 96(1-3), 187–207 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Heußner, A.: Model checking communicating processes: Run graphs, graph grammars, and MSO. ECEASST 47 (2012)Google Scholar
  16. 16.
    ITU-TS. ITU-TS Recommendation Z.120: Message Sequence Chart (MSC). ITU-TS, Geneva (February 2011)Google Scholar
  17. 17.
    La Torre, S., Madhusudan, P., Parlato, G.: A robust class of context-sensitive languages. In: LICS, pp. 161–170. IEEE Computer Society (2007)Google Scholar
  18. 18.
    La Torre, S., Madhusudan, P., Parlato, G.: An infinite automaton characterization of double exponential time. In: Kaminski, M., Martini, S. (eds.) CSL 2008. LNCS, vol. 5213, pp. 33–48. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    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
  20. 20.
    Madhusudan, P., Parlato, G.: The tree width of auxiliary storage. In: Ball, T., Sagiv, M. (eds.) POPL, pp. 283–294. ACM (2011)Google Scholar
  21. 21.
    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
  22. 22.
    Vardi, M.Y.: The taming of converse: Reasoning about two-way computations. In: Parikh, R. (ed.) Logics of Programs. LNCS, vol. 193, pp. 413–423. Springer, Heidelberg (1985)CrossRefGoogle Scholar
  23. 23.
    Zielonka, W.: Notes on finite asynchronous automata. R.A.I.R.O. — Informatique Théorique et Applications 21, 99–135 (1987)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • C. Aiswarya
    • 1
  • Paul Gastin
    • 2
  • K. Narayan Kumar
    • 3
  1. 1.Uppsala UniversitySweden
  2. 2.LSV, ENS Cachan, CNRS & INRIAFrance
  3. 3.Chennai Mathematical InstituteIndia

Personalised recommendations