Model Checking Languages of Data Words

  • Benedikt Bollig
  • Aiswarya Cyriac
  • Paul Gastin
  • K. Narayan Kumar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7213)

Abstract

We consider the model-checking problem for data multi-pushdown automata (DMPA). DMPA generate data words, i.e, strings enriched with values from an infinite domain. The latter can be used to represent an unbounded number of process identifiers so that DMPA are suitable to model concurrent programs with dynamic process creation. To specify properties of data words, we use monadic second-order (MSO) logic, which comes with a predicate to test two word positions for data equality. While satisfiability for MSO logic is undecidable (even for weaker fragments such as first-order logic), our main result states that one can decide if all words generated by a DMPA satisfy a given formula from the full MSO logic.

Keywords

Model Check Transitive Closure Concurrent Program Data Equality Unbounded Number 
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.

References

  1. 1.
    Abdulla, P.A.: Forcing Monotonicity in Parameterized Verification: From Multisets to Words. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds.) SOFSEM 2010. LNCS, vol. 5901, pp. 1–15. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Bojańczyk, M., David, C., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on data words. ACM Trans. Comput. Log. 12(4), 27 (2011)MathSciNetGoogle Scholar
  3. 3.
    Bojańczyk, M., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on data trees and applications to XML reasoning. J. ACM 56(3) (2009)Google Scholar
  4. 4.
    Bollig, B.: An automaton Over Data Words that Captures EMSO Logic. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011 – Concurrency Theory. LNCS, vol. 6901, pp. 171–186. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Bollig, B., Hélouët, L.: Realizability of Dynamic MSC Languages. In: Ablayev, F.M., Mayr, E.W. (eds.) CSR 2010. LNCS, vol. 6072, pp. 48–59. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Cheng, E.Y.C., Kaminski, M.: Context-free languages over infinite alphabets. Acta Inf. 35(3), 245–267 (1998)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Courcelle, B.: Graph rewriting: an algebraic and logic approach. In: Handbook of Theoretical Computer Science, vol. B, pp. 193–242. MIT Press (1990)Google Scholar
  8. 8.
    David, C., Libkin, L., Tan, T.: On the Satisfiability of Two-Variable Logic Over Data Words. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 248–262. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Demri, S., Lazić, R.: LTL with the freeze quantifier and register automata. ACM Transactions on Computational Logic 10(3) (2009)Google Scholar
  10. 10.
    Demri, S., Lazić, R., Sangnier, A.: Model Checking Freeze LTL Over One-Counter Automata. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 490–504. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  11. 11.
    Demri, S., Sangnier, A.: When Model-Checking Freeze LTL over Counter Machines Becomes Decidable. In: Ong, C.-H.L. (ed.) FOSSACS 2010. LNCS, vol. 6014, pp. 176–190. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Grumberg, O., Kupferman, O., Sheinvald, S.: Variable Automata over Infinite Alphabets. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 561–572. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Kaminski, M., Francez, N.: Finite-memory automata. Theoretical Computer Science 134(2), 329–363 (1994)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Kaminski, M., Zeitlin, D.: Finite-memory automata with non-deterministic reassignment. Int. J. Found. Comput. Sci. 21(5), 741–760 (2010)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    La Torre, S., Madhusudan, P., Parlato, G.: A robust class of context-sensitive languages. In: LICS 2007, pp. 161–170. IEEE Computer Society Press (2007)Google Scholar
  16. 16.
    La Torre, S., Madhusudan, P., Parlato, G.: Context-Bounded Analysis of Concurrent Queue Systems. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 299–314. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    Leucker, M., Madhusudan, P., Mukhopadhyay, S.: Dynamic Message Sequence Charts. In: Agrawal, M., Seth, A.K. (eds.) FSTTCS 2002. LNCS, vol. 2556, pp. 253–264. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Madhusudan, P., Parlato, G.: The tree width of auxiliary storage. In: Ball, T., Sagiv, M. (eds.) POPL 2011, pp. 283–294. ACM (2011)Google Scholar
  19. 19.
    Niewerth, M., Schwentick, T.: Two-variable logic and key constraints on data words. In: Milo, T. (ed.) ICDT 2011, pp. 138–149. ACM (2011)Google Scholar
  20. 20.
    Tzevelekos, N.: Fresh-register automata. In: Ball, T., Sagiv, M. (eds.) POPL 2011, pp. 295–306. ACM (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Benedikt Bollig
    • 1
  • Aiswarya Cyriac
    • 1
  • Paul Gastin
    • 1
  • K. Narayan Kumar
    • 2
  1. 1.LSV, ENS Cachan, CNRS & INRIAFrance
  2. 2.Chennai Mathematical InstituteIndia

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