Advertisement

An Extension of Pushdown System and Its Model Checking Method

  • Naoya Nitta
  • Hiroyuki Seki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2761)

Abstract

In this paper, we present a class of infinite transition systems which is an extension of pushdown systems (PDS), and show that LTL (linear temporal logic) model checking for the class is decidable. Since the class is defined as a subclass of term rewriting systems, pushdown stack of PDS is naturally extended to tree structure. By this extension, we can model recursive programs with exception handling.

Keywords

Model Check Transitive Closure Linear Temporal Logic Exception Handling Tree Automaton 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)Google Scholar
  2. 2.
    Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)Google Scholar
  3. 3.
    Coquidé, J.L., Dauchet, M., Gilleron, R., Vágv”olgyi, S.: Bottom-up tree pushdown automata: classification and connection with rewrite systems. Theoretical Computer Science 127, 69–98 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Corbett, J.C., Dwyer, M.B., Hatcliff, J., Laubach, S., Păsăreanu, C.S., Robby, J., Zheng, H.: Bandera: Extracting finite-state models from Java source code, Int’l Conf. on Software Engineering, pp. 439–448 (2000)Google Scholar
  5. 5.
    Esparza, J., Hansel, D., Rossmanith, P., Schwoon, S.: Efficient algorithms for model-checking pushdown systems. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 232–247. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  6. 6.
    Esparza, J., Kučera, A., Schwoon, S.: Model-checking LTL with regular variations for pushdown systems. In: Kobayashi, N., Pierce, B.C. (eds.) TACS 2001. LNCS, vol. 2215, pp. 316–339. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Esparza, J., Schwoon, S.: A BDD-based model checker for recursive programs. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 324–336. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Gécseq, F., Steinby, M.: Tree Automata, Académiai Kiadó (1984)Google Scholar
  9. 9.
    Gilleron, R.: Decision problems for term rewriting systems and recognizable tree languages. In: Jantzen, M., Choffrut, C. (eds.) STACS 1991. LNCS, vol. 480, pp. 148–159. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  10. 10.
    Gilleron, R., Tison, S.: Regular tree languages and rewrite systems. Fundamenta Informaticae 24, 157–175 (1995)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Graf, S., Saïdi, H.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)Google Scholar
  12. 12.
    Gyenizse, P., Vágvölgyi, S.: Linear generalized semi-monadic rewrite systems effectively preserve recognizability. Theoretical Computer Science 194, 87–122 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Jensen, T., Le Métayer, D., Thorn, T.: Verification of control flow based security properties. In: IEEE Symp. on Security and Privacy, pp. 89–103 (1999)Google Scholar
  14. 14.
    Jha, S., Reps, T.: Analysis of SPKI/SDSI certificates using model checking. In: IEEE Computer Security Foundations Workshop, pp. 129–144 (2002)Google Scholar
  15. 15.
    Löding, C.: Model-checking infinite systems generated by ground tree rewriting. In: Nielsen, M., Engberg, U. (eds.) FOSSACS 2002. LNCS, vol. 2303, pp. 280–294. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Mayr, R.: Process rewrite systems. Inform. & Comput. 156, 264–286 (1999)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Nagaya, T., Toyama, Y.: Decidability for left-linear growing term rewriting systems. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, pp. 256–270. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  18. 18.
    Nitta, N., Seki, H.: An extension of pushdown system and its model checking method, Technical Report, Nara Institute of Science and Technology (2003)Google Scholar
  19. 19.
    Nitta, N., Takata, Y., Seki, H.: Security verification of programs with stack inspection. In: 6th ACM Symp. on Access Control Models and Technologies, pp. 31–40 (2001)Google Scholar
  20. 20.
    Nitta, N., Takata, Y., Seki, H.: An efficient security verification method for programs with stack inspection. In: 8th ACM Conf. on Computer and Communication Security, pp. 68–77 (2001)Google Scholar
  21. 21.
    Obdržálek, J.: Model checking Java using pushdown systems. In: ECOOP Workshop on Formal Techniques for Java-like Programs (2002)Google Scholar
  22. 22.
  23. 23.
    Takai, T., Kaji, Y., Seki, H.: Right-linear finite path overlapping term rewriting systems effectively preserve recognizability. In: Bachmair, L. (ed.) RTA 2000. LNCS, vol. 1833, pp. 246–260. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  24. 24.
    Walukiewicz, I.: Pushdown processes: Games and model-checking. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 62–74. Springer, Heidelberg (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Naoya Nitta
    • 1
  • Hiroyuki Seki
    • 1
  1. 1.Nara Institute of Science and TechnologyIkoma, NaraJapan

Personalised recommendations