Resource-Constrained Model Checking of Recursive Programs

  • Samik Basu
  • K. Narayan Kumar
  • L. Robert Pokorny
  • C. R. Ramakrishnan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2280)

Abstract

A number of recent papers present efficient algorithms for LTL model checking for recursive programs with finite data structures. A common feature in all these works is that they consider infinitely long runs of the program without regard to the size of the program stack. Runs requiring unbounded stack are often a result of abstractions done to obtain a finite-data recursive program. In this paper, we introduce the notion of resource-constrained model checking where we distinguish between stack-diverging runs and finite-stack runs. It should be noted that finiteness of stack-like resources cannot be expressed in LTL. We develop resource-constrained model checking in terms of good cycle detection in a finite graph called R-graph, which is constructed from a given push-down system (PDS) and a Büchi automaton. We make the formulation of the model checker “executable” by encoding it directly as Horn clauses. We present a local algorithm to detect a good cycle in an R-graph. Furthermore, by describing the construction of R-graph as a logic program and evaluating it using tabled resolution, we do model checking without materializing the push-down system or the induced Rgraph. Preliminary experiments indicate that the local model checker is at least as efficient as existing model checkers for push-down systems.

Keywords

Model Check Logic Program Horn Clause Good Cycle Symbolic Model Checker 
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.
    R. Alur, K. Etessami, and M. Yannakakis. Analysis of recursive state machines. In Computer-Aided Verification (CAV 2001). Springer-Verlag, 2001.Google Scholar
  2. 2.
    T. Ball and S. Rajamani. Bebop: A symbolic model checker for boolean programs. In SPIN00: SPIN Workshop, volume 1885 of Lecture Notes in Computer Science, pages 113–130, 2000.Google Scholar
  3. 3.
    M. Benedikt, P. Godefroid, and T. Reps. Model checking unrestricted hierarchical state machines. In Twenty-Eighth Int. Colloq. on Automata, Languages, and Programming(ICALP 2001). Springer-Verlag, 2001.Google Scholar
  4. 4.
    A. Bouajjani, J. Esparza, and O. Maler. Reachability analysis of pushdown automata: Application to model checking. In Concurrency Theory (CONCURR 1997), 1997.Google Scholar
  5. 5.
    O. Burkart and B. Steffen. Model checking the full-modal mu-calculus for infinite sequential processes. In Proceedings of ICALP’97, volume 1256 of Lecture Notes in Computer Science, pages 419–429, 1997.Google Scholar
  6. 6.
    W. Chen and D. S. Warren. Tabled evaluation with delaying for general logic programs. Journal of the ACM, 43(1):20–74, January 1996.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    E. M. Clarke and E. A. Emerson. Design and synthesis of synchronization skeletons using branching-time temporal logic. In D. Kozen, editor, Proceedings of the Workshop on Logic of Programs, Yorktown Heights, volume 131 of Lecture Notes in Computer Science, pages 52–71. Springer Verlag, 1981.Google Scholar
  8. 8.
    E. M. Clarke, E. A. Emerson, and A. P. Sistla. Automatic verification of finitestate concurrent systems using temporal logic specifications. ACM TOPLAS, 8(2), 1986.Google Scholar
  9. 9.
    J.-M. Couvreur. On-the-fly verification of linear temporal logic. In Proceedings of FM’99, volume 1708 of Lecture Notes in Computer Science, pages 253–271, 1999.Google Scholar
  10. 10.
    J. Esparza, D. Hansel, P. Rossmanith, and S. Schwoon. Efficient algorithms for model checking pushdown systems. In Computer-Aided Verification (CAV 2000), pages 232–247. Springer-Verlag, 2000.Google Scholar
  11. 11.
    J. Esparza and S. Schwoon. A bdd-based model checker for recursive programs. In Computer-Aided Verification (CAV 2001), pages 324–336. Springer-Verlag, 2001.Google Scholar
  12. 12.
    A. Finkel, B. Willems, and P. Wolper. A direct symbolic approach to model checking pushdown systems. In Second International Workshop on Verification of Infinite State Systems(INFINITY 1997), volume 9. Elsevier Science, 1997.Google Scholar
  13. 13.
    L.R. Pokorny and C.R. Ramakrishnan. LTL model checking using tabled logic programming. In Workshop on Tabling in Parsing and Deduction, 2000. Available from http://www.cs.sunysb.edu/~cram/papers.
  14. 14.
    J. P. Queille and J. Sifakis. Specification and verification of concurrent systems in Cesar. In Proceedings of the International Symposium in Programming, volume 137 of Lecture Notes in Computer Science, Berlin, 1982. Springer-Verlag.Google Scholar
  15. 15.
    T. Reps, S. Horwitz, and M. Sagiv. Precise interprocedural dataflow analysis via graph reachability. In Twenty-Second ACM Symposium on Principles of Programming Languages, pages 49–61, 1995.Google Scholar
  16. 16.
    D. A. Schmidt and B. Steffen. Program analysis as model checking of abstract interpretations. In Static Analysis Symposium, pages 351–380, 1998.Google Scholar
  17. 17.
    H. Tamaki and T. Sato. OLDT resolution with tabulation. In International Conference on Logic Programming, pages 84–98. MIT Press, 1986.Google Scholar
  18. 18.
    R. E. Tarjan. Depth first search and linear graph algorithms. SIAM Journal of Computing, 1(2):146–160, 1972.MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    XSB. The XSB logic programming system. Available from http://xsb.sourceforge.net.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Samik Basu
    • 1
  • K. Narayan Kumar
    • 1
    • 2
  • L. Robert Pokorny
    • 1
  • C. R. Ramakrishnan
    • 1
  1. 1.Department of Computer ScienceState University of New York at Stony BrookNew YorkUSA
  2. 2.Chennai Mathematical InstituteChennaiIndia

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