Model-Checking Linear-Time Properties of Parametrized Asynchronous Shared-Memory Pushdown Systems

  • Marie Fortin
  • Anca Muscholl
  • Igor WalukiewiczEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10427)


A parametrized verification problem asks if a parallel composition of a leader process with some number of copies of a contributor process can exhibit a behavior satisfying a given property. We focus on the case of pushdown processes communicating via shared memory. In a series of recent papers it has been shown that reachability in this model is Pspace-complete [Hague’11], [Esparza, Ganty, Majumdar’13], and that liveness is decidable in Nexptime [Durand-Gasselin, Esparza, Ganty, Majumdar’15]. We show that verification of general regular properties of traces of executions, satisfying some stuttering condition, is Nexptime-complete for this model. We also study two interesting subcases of this problem: we show that liveness is actually Pspace-complete, and that safety is already Nexptime-complete.


  1. 1.
    Atig, M.F., Bouajjani, A., Qadeer, S.: Context-bounded analysis for concurrent programs with dynamic creation of threads. Log. Methods Comput. Sci. 7(4), 1–48 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Ball, T., Chaki, S., Rajamani, S.K.: Parameterized verification of multithreaded software libraries. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 158–173. Springer, Heidelberg (2001). doi: 10.1007/3-540-45319-9_12 CrossRefGoogle Scholar
  3. 3.
    Bloem, R., Jacobs, S., Khalimov, A., Konnov, I., Rubin, S., Veith, H., Widder, J.: Decidability of Parameterized Verification. Morgan & Claypool Publishers, San Rafael (2015)Google Scholar
  4. 4.
    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). doi: 10.1007/3-540-63141-0_10 Google Scholar
  5. 5.
    Bouajjani, A., Esparza, J., Schwoon, S., Strejĉek, J.: Reachability analysis of multithreaded software with asynchronous communication. In: Sarukkai, S., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 348–359. Springer, Heidelberg (2005). doi: 10.1007/11590156_28 CrossRefGoogle Scholar
  6. 6.
    Bouajjani, A., Müller-Olm, M., Touili, T.: Regular symbolic analysis of dynamic networks of pushdown systems. In: Abadi, M., Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 473–487. Springer, Heidelberg (2005). doi: 10.1007/11539452_36 CrossRefGoogle Scholar
  7. 7.
    Bouyer, P., Markey, N., Randour, M., Sangnier, A., Stan, D.: Reachability in networks of register protocols under stochastic schedulers. In: ICALP 2016, LIPIcs, pp. 106:1–106:14. Leibniz-Zentrum für Informatik (2016)Google Scholar
  8. 8.
    Chadha, R., Madhusudan, P., Viswanathan, M.: Reachability under contextual locking. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 437–450. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-28756-5_30 CrossRefGoogle Scholar
  9. 9.
    Clarke, E.M., Grumberg, O., Jha, S.: Verifying parameterized networks. ACM Trans. Program. Lang. Syst. 19(5), 726–750 (1997)CrossRefGoogle Scholar
  10. 10.
    Courcelle, B.: On constructing obstruction sets of words. Bull. EATCS 44, 178–186 (1991)zbMATHGoogle Scholar
  11. 11.
    Delzanno, G.: Parameterized verification and model checking for distributed broadcast protocols. In: Giese, H., König, B. (eds.) ICGT 2014. LNCS, vol. 8571, pp. 1–16. Springer, Cham (2014). doi: 10.1007/978-3-319-09108-2_1 Google Scholar
  12. 12.
    Durand-Gasselin, A., Esparza, J., Ganty, P., Majumdar, R.: Model checking parameterized asynchronous shared-memory systems. Form. Methods Syst. Des. 50(2–3), 140–167 (2017). Journal version of CAV 2015CrossRefzbMATHGoogle Scholar
  13. 13.
    Emerson, E.A., Kahlon, V.: Model checking guarded protocols. In: LICS 2003, pp. 361–370 (2003)Google Scholar
  14. 14.
    Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: LICS 1999, pp. 352–359. IEEE (1999)Google Scholar
  15. 15.
    Esparza, J., Ganty, P., Majumdar, R.: Parameterized verification of asynchronous shared-memory systems. J. ACM 63(1), 10:1–10:48 (2016). Journal version of CAV 2013MathSciNetCrossRefGoogle Scholar
  16. 16.
    Etessami, K.: A note on a question of Peled and Wilke regarding stutter-invariant LTL. Inf. Process. Lett. 75(6), 261–263 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Fortin, M., Muscholl, A., Walukiewicz, I.: On parametrized verification of asynchronous, shared-memory pushdown systems. CoRR, abs/1606.08707 (2016)Google Scholar
  18. 18.
    Fürer, M.: The computational complexity of the unconstrained limited domino problem (with implications for logical decision problems). In: Börger, E., Hasenjaeger, G., Rödding, D. (eds.) LaM 1983. LNCS, vol. 171, pp. 312–319. Springer, Heidelberg (1984). doi: 10.1007/3-540-13331-3_48 CrossRefGoogle Scholar
  19. 19.
    German, S.A., Sistla, P.A.: Reasoning about systems with many processes. J. ACM 39(3), 675–735 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Hague, M.: Parameterised pushdown systems with non-atomic writes. In: FSTTCS 2011. LIPIcs, pp. 457–468. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)Google Scholar
  21. 21.
    Kahlon, V.: Parameterization as abstraction: a tractable approach to the dataflow analysis of concurrent programs. In: LICS 2008, pp. 181–192. IEEE (2008)Google Scholar
  22. 22.
    Kahlon, V., Ivančić, F., Gupta, A.: Reasoning about threads communicating via locks. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 505–518. Springer, Heidelberg (2005). doi: 10.1007/11513988_49 CrossRefGoogle Scholar
  23. 23.
    Kaiser, A., Kroening, D., Wahl, T.: Dynamic cutoff detection in parameterized concurrent programs. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 645–659. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-14295-6_55 CrossRefGoogle Scholar
  24. 24.
    Kesten, Y., Pnueli, A., Shahar, E., Zuck, L.: Network invariants in action*. In: Brim, L., Křetínský, M., Kučera, A., Jančar, P. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 101–115. Springer, Heidelberg (2002). doi: 10.1007/3-540-45694-5_8 CrossRefGoogle Scholar
  25. 25.
    La Torre, S., Madhusudan, P., Parlato, G.: Model-checking parameterized concurrent programs using linear interfaces. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 629–644. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-14295-6_54 CrossRefGoogle Scholar
  26. 26.
    La Torre, S., Madhusudan, P., Parlato, G.: Sequentializing parameterized programs. In: FIT 2012. EPTCS, vol. 87, pp. 34–47 (2012)Google Scholar
  27. 27.
    La Torre, S., Muscholl, A., Walukiewicz, I.: Safety of parametrized asynchronous shared-memory systems is almost always decidable. In: CONCUR 2015. LIPIcs, vol. 42, pp. 72–84. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)Google Scholar
  28. 28.
    Lammich, P., Müller-Olm, M.: Conflict analysis of programs with procedures, dynamic thread creation, and monitors. In: Alpuente, M., Vidal, G. (eds.) SAS 2008. LNCS, vol. 5079, pp. 205–220. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-69166-2_14 CrossRefGoogle Scholar
  29. 29.
    Lammich, P., Müller-Olm, M., Seidl, H., Wenner, A.: Contextual locking for dynamic pushdown networks. In: Logozzo, F., Fähndrich, M. (eds.) SAS 2013. LNCS, vol. 7935, pp. 477–498. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-38856-9_25 CrossRefGoogle Scholar
  30. 30.
    Lammich, P., Müller-Olm, M., Wenner, A.: Predecessor sets of dynamic pushdown networks with tree-regular constraints. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 525–539. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-02658-4_39 CrossRefGoogle Scholar
  31. 31.
    Lin, A.W., Rümmer, P.: Liveness of randomised parameterised systems under arbitrary schedulers. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9780, pp. 112–133. Springer, Cham (2016). doi: 10.1007/978-3-319-41540-6_7 Google Scholar
  32. 32.
    Muscholl, A., Seidl, H., Walukiewicz, I.: Reachability for dynamic parametric processes. In: Bouajjani, A., Monniaux, D. (eds.) VMCAI 2017. LNCS, vol. 10145, pp. 424–441. Springer, Cham (2017). doi: 10.1007/978-3-319-52234-0_23 CrossRefGoogle Scholar
  33. 33.
    Namjoshi, K.S., Trefler, R.J.: Analysis of dynamic process networks. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 164–178. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-46681-0_11 Google Scholar
  34. 34.
    Peled, D.A., Wilke, T.: Stutter-invariant temporal properties are expressible without the next-time operator. Inf. Process. Lett. 63(5), 243–246 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Ramalingam, G.: Context-sensitive synchronization-sensitive analysis is undecidable. ACM Trans. Program. Lang. Syst. (TOPLAS) 22(2), 416–430 (2000)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.LSV, CNRS, ENS Paris-SaclayUniversité Paris-SaclayCachanFrance
  2. 2.LaBRIUniversity of BordeauxBordeauxFrance
  3. 3.CNRS, LaBRIUniversity of BordeauxBordeauxFrance

Personalised recommendations