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A Complete Bounded Model Checking Algorithm for Pushdown Systems

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Hardware and Software: Verification and Testing (HVC 2007)

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Abstract

Pushdown systems (PDSs) consist of a stack and a finite state machine and are frequently used to model abstractions of software. They correspond to sequential recursive programs with finite-domain variables. This paper presents a novel algorithm for deciding reachability of particular locations of PDSs. We exploit the fact that most PDSs used in practice are shallow, and propose to use SAT-based Bounded Model Checking to search for counterexamples. Completeness is achieved by computing universal summaries of the procedures in the program.

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References

  1. Ball, T., Rajamani, S.K.: Bebop: A symbolic model checker for Boolean programs. In: Havelund, K., Penix, J., Visser, W. (eds.) SPIN 2000. LNCS, vol. 1885, pp. 113–130. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  2. Ball, T., et al.: SLAM and Static Driver Verifier: Technology transfer of formal methods inside Microsoft. In: Boiten, E.A., Derrick, J., Smith, G.P. (eds.) IFM 2004. LNCS, vol. 2999, pp. 1–20. Springer, Heidelberg (2004)

    Google Scholar 

  3. Sharir, M., Pnueli, A.: Two approaches to interprocedural dataflow analysis. In: Program Flow Analysis: Theory and Applications, pp. 189–233. Prentice-Hall, Englewood Cliffs (1981)

    Google Scholar 

  4. Finkel, A., Willems, B., Wolper, P.: A direct symbolic approach to model checking pushdown systems. In: Workshop on Verification of Infinite State Systems (INFINITY). ENTCS, vol. 9, pp. 27–39 (1997)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  6. Basler, G., Kroening, D., Weissenbacher, G.: SAT-based summarisation for Boolean programs. In: Bošnački, D., Edelkamp, S. (eds.) SPIN 2007. LNCS, vol. 4595, pp. 131–148. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  7. Schwoon, S.: Model-Checking Pushdown Systems. PhD thesis, Technische Universität München (2002)

    Google Scholar 

  8. Büchi, J.R.: Regular canonical systems. Archive for Mathematical Logic 6, 91 (1964)

    Article  MATH  Google Scholar 

  9. Ball, T., Rajamani, S.: Boolean programs: A model and process for software analysis. Technical Report 2000-14, Microsoft Research (2000)

    Google Scholar 

  10. Ball, T., Majumdar, R., Millstein, T., Rajamani, S.K.: Automatic predicate abstraction of C programs. In: Programming Language Design and Implementation (PLDI), pp. 203–213. ACM Press, New York (2001)

    Google Scholar 

  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. Leino, K.R.M.: A SAT characterization of Boolean-program correctness. In: Ball, T., Rajamani, S.K. (eds.) SPIN 2003. LNCS, vol. 2648, pp. 104–120. Springer, Heidelberg (2003)

    Google Scholar 

  13. Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)

    Google Scholar 

  14. Kroening, D., Strichman, O.: Efficient computation of recurrence diameters. In: Zuck, L.D., Attie, P.C., Cortesi, A., Mukhopadhyay, S. (eds.) VMCAI 2003. LNCS, vol. 2575, pp. 298–309. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  15. Alur, R., Benedikt, M., Etessami, K., Godefroid, P., Reps, T., Yannakakis, M.: Analysis of recursive state machines. ACM Transactions on Programming Languages and Systems (TOPLAS) 27, 786–818 (2005)

    Article  Google Scholar 

  16. Cook, B., Kroening, D., Sharygina, N.: Symbolic model checking for asynchronous Boolean programs. In: Godefroid, P. (ed.) SPIN 2005. LNCS, vol. 3639, pp. 75–90. Springer, Heidelberg (2005)

    Google Scholar 

  17. 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)

    Google Scholar 

  18. Touili, T., Sighireanu, M.: Bounded communication reachability analysis of process rewrite systems with ordered parallelism. In: Verification of Infinite State Systems (INFINITY). ENTCS, Elsevier, Amsterdam (2006)

    Google Scholar 

  19. Cook, B., Kroening, D., Sharygina, N.: Over-Approximating Boolean Programs with unbounded thread creation. In: Formal Methods in Computer-Aided Design FMCAD, pp. 53–59. IEEE Computer Society Press, Los Alamitos (2006)

    Chapter  Google Scholar 

  20. Bouajjani, A., Esparza, J., Touili, T.: A generic approach to the static analysis of concurrent programs with procedures. In: Principles of Programming Languages (POPL), pp. 62–73. ACM Press, New York (2003)

    Chapter  Google Scholar 

  21. Lal, A., Reps, T.: Improving pushdown system model checking. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 343–357. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  22. Bouajjani, A., Esparza, J.: Rewriting models of Boolean programs. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  23. Biere, A., Cimatti, A., Clarke, E.M., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) ETAPS 1999 and TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  24. Xie, Y., Aiken, A.: Saturn: A scalable framework for error detection using boolean satisfiability. ACM Transactions on Programming Languages and Systems (TOPLAS) 29 (2007)

    Google Scholar 

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Karen Yorav

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Basler, G., Kroening, D., Weissenbacher, G. (2008). A Complete Bounded Model Checking Algorithm for Pushdown Systems. In: Yorav, K. (eds) Hardware and Software: Verification and Testing. HVC 2007. Lecture Notes in Computer Science, vol 4899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77966-7_17

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  • DOI: https://doi.org/10.1007/978-3-540-77966-7_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77964-3

  • Online ISBN: 978-3-540-77966-7

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