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Abstract

Software model-checking based on the CEGAR framework can be made more precise by separating non-determinism from the lack of information due to abstraction. The two can be modeled individually using four-valued Belnap logic. In addition, this logic allows reasoning about negations effectively and thus enables checking of full CTL. In this paper, we present Yasm – a new symbolic software model-checker. Preliminary experience with Yasm shows that our implementation can effectively construct and analyze Belnap models without a substantial overhead when compared to its classical counterparts.

Keywords

Model Check Transition Relation Atomic Proposition Kripke Structure Control Flow Graph 
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.
    Ball, T., Podelski, A., Rajamani, S.: Boolean and Cartesian Abstraction for Model Checking C Programs. STTT 5(1), 49–58 (2003)CrossRefMATHGoogle Scholar
  2. 2.
    Ball, T., Rajamani, S.: The SLAM Toolkit. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 260–264. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Barrett, C., Berezin, S.: CVC Lite: A New Implementation of the Cooperating Validity Checker. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 515–518. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Belnap, N.D.: A Useful Four-Valued Logic. In: Dunn, Epstein (eds.) Modern Uses of Multiple-Valued Logic, pp. 30–56. Reidel (1977)Google Scholar
  5. 5.
    Chechik, M., Gurfinkel, A., Devereux, B.: χChek: A multi-valued model-checker. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 505–509. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-Guided Abstraction Refinement for Symbolic Model Checking. Journal of the ACM 50(5), 752–794 (2003)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  8. 8.
    Dams, D., Gerth, R., Grumberg, O.: Abstract Interpretation of Reactive Systems. ACM TOPLAS 2(19), 253–291 (1997)CrossRefGoogle Scholar
  9. 9.
    de Alfaro, L., Godefroid, P., Jagadeesan, R.: Three-Valued Abstractions of Games: Uncertainty, but with Precision. In: Proceedings of LICS 2004, pp. 170–179 (2004)Google Scholar
  10. 10.
    Godefroid, P.: Reasoning about Abstract Open Systems with Generalized Module Checking. In: Alur, R., Lee, I. (eds.) EMSOFT 2003. LNCS, vol. 2855, pp. 223–240. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Godefroid, P., Huth, M., Jagadeesan, R.: Abstraction-based Model Checking using Modal Transition Systems. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 426–440. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Godefroid, P., Jagadeesan, R.: Automatic Abstraction Using Generalized Model-Checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 137–150. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    Grumberg, O., Lange, M., Leucker, M., Shoham, S.: Don’t Know in the ì-Calculus. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 233–249. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Gurfinkel, A., Chechik, M.: Generating Counterexamples for Multi-Valued Model-Checking. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805. Springer, Heidelberg (2003)Google Scholar
  16. 16.
    Gurfinkel, A., Chechik, M.: Multi-Valued Model-Checking via Classical Model-Checking. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 263–277. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  17. 17.
    Gurfinkel, A., Chechik, M.: How thorough is thorough enough? In: Borrione, D., Paul, W. (eds.) CHARME 2005. LNCS, vol. 3725, pp. 65–80. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Gurfinkel, A., Wei, O., Chechik, M.: Systematic construction of abstractions for model-checking. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 381–397. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
    Hazelhurst, S., Seger, C.H.: Model Checking Lattices: Using and Reasoning about Information Orders for Abstraction. Logic Journal of the IGPL 7(3), 375–411 (1999)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Henzinger, T., Jhala, R., Majumdar, R., Sutre, G.: Lazy Abstraction. In: Proceedings of POPL 2002, pp. 58–70 (2002)Google Scholar
  21. 21.
    Henzinger, T.A., Jhala, R., Majumdar, R., McMillan, K.L.: Abstractions from Proofs. In: Proceedings of POPL 2004, pp. 232–244 (2004)Google Scholar
  22. 22.
    Kleene, S.C.: Introduction to Metamathematics. Van Nostrand, New York (1952)MATHGoogle Scholar
  23. 23.
    Kozen, D.: Results on the Propositional ì-calculus. Theoretical Computer Science 27, 334–354 (1983)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Larsen, K.G., Xinxin, L.: Equation Solving Using Modal Transition Systems. In: Proceedings of LICS 1990 (1990)Google Scholar
  25. 25.
    Pasareanu, C., Dwyer, M., Visser, W.: Finding Feasible Counter-examples when Model Checking Abstracted Java Programs. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 284–298. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  26. 26.
    Reps, T.W., Sagiv, M., Wilhelm, R.: Static Program Analysis via 3-Valued Logic. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 15–30. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  27. 27.
    Shoham, S., Grumberg, O.: Monotonic abstraction-refinement for CTL. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 546–560. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  28. 28.
    Somenzi, F.: CUDD: CU Decision Diagram Package Release (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Arie Gurfinkel
    • 1
  • Marsha Chechik
    • 1
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada

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