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Abstract Model Checking without Computing the Abstraction

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FM 2009: Formal Methods (FM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5850))

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Abstract

Abstraction is a fundamental technique that enables the verification of large systems. In symbolic model checking, abstractions are defined by formulas that relate concrete and abstract variables. In predicate abstraction, the abstract variables are equivalent to some predicates over the concrete variables.

In order to apply model checking on the abstract state space, it is usually necessary to compute a quantifier-free formula that is equivalent to the abstract transition relation. In predicate abstraction, the quantifier elimination can be obtained by solving an ALLSAT problem. In many practical cases, this computation results into a bottleneck.

In this paper, we propose a new algorithm that combines abstraction with bounded model checking and k-induction. The algorithm does not rely on quantifier elimination, but encodes the model checking problem over the abstract state space into SAT problems. The algorithm is a novelty in the state-of-the-art of abstract model checking because it avoids computing the abstraction. An experimental evaluation with case studies taken from an industrial project shows that the new algorithm is more efficient and reaches in some cases a time improvement that is exponential in the number of predicates.

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References

  1. Ball, T., Podelski, A., Rajamani, S.K.: Boolean and Cartesian abstraction for model checking C programs. STTT 5(1), 49–58 (2003)

    Google Scholar 

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

    Chapter  Google Scholar 

  3. Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic Model Checking: 1020 States and Beyond. Inf. and Comp. 98(2), 142–170 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cavada, R., Cimatti, A., Franzén, A., Kalyanasundaram, K., Roveri, M., Shyamasundar, R.K.: Computing predicate abstractions by integrating BDDs and SMT solvers. In: FMCAD, pp. 69–76. IEEE, Los Alamitos (2007)

    Google Scholar 

  5. Cimatti, A., Roveri, M., Susi, A., Tonetta, S.: Object models with temporal constraints. Journal of Software and Systems Modeling (SoSyM), http://www.springerlink.com/content/46244553v27695l1/ , doi: 10.1007/s10270-009-0130-7

  6. Cimatti, A., Roveri, M., Tonetta, S.: Requirements Validation for Hybrid Systems. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 188–203. Springer, Heidelberg (2009)

    Google Scholar 

  7. Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-Guided Abstraction Refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  8. Clarke, E.M., Grumberg, O., Long, D.E.: Model Checking and Abstraction. ACM Trans. Program. Lang. Syst. 16(5), 1512–1542 (1994)

    Article  Google Scholar 

  9. Clarke, E.M., Gupta, A., Kukula, J.H., Strichman, O.: SAT Based Abstraction-Refinement Using ILP and Machine Learning Techniques. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 265–279. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Clarke, E.M., Kroening, D., Sharygina, N., Yorav, K.: Predicate Abstraction of ANSI-C Programs Using SAT. FMSD 25(2-3), 105–127 (2004)

    MATH  Google Scholar 

  11. Colón, M., Uribe, T.E.: Generating Finite-State Abstractions of Reactive Systems Using Decision Procedures. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 293–304. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  12. Das, S., Dill, D.L.: Successive Approximation of Abstract Transition Relations. In: LICS, pp. 51–60 (2001)

    Google Scholar 

  13. Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. Electr. Notes Theor. Comput. Sci. 89(4) (2003)

    Google Scholar 

  14. Emerson, E.A., Clarke, E.M.: Using Branching Time Temporal Logic to Synthesize Synchronization Skeletons. Sci. Comput. Program 2(3), 241–266 (1982)

    Article  MATH  Google Scholar 

  15. 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 

  16. Gupta, A., Strichman, O.: Abstraction Refinement for Bounded Model Checking. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 112–124. Springer, Heidelberg (2005)

    Google Scholar 

  17. Henzinger, T.A., Jhala, R., Majumdar, R., Sutre, G.: Lazy abstraction. In: POPL, pp. 58–70 (2002)

    Google Scholar 

  18. Kroening, D., Sharygina, N., Tonetta, S., Tsitovich, A., Wintersteiger, C.M.: Loop Summarization Using Abstract Transformers. In: Cha, S(S.), Choi, J.-Y., Kim, M., Lee, I., Viswanathan, M. (eds.) ATVA 2008. LNCS, vol. 5311, pp. 111–125. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Lahiri, S.K., Bryant, R.E., Cook, B.: A Symbolic Approach to Predicate Abstraction. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 141–153. Springer, Heidelberg (2003)

    Google Scholar 

  20. Li, B., Wang, C., Somenzi, F.: Abstraction refinement in symbolic model checking using satisfiability as the only decision procedure. STTT 7(2), 143–155 (2005)

    Article  Google Scholar 

  21. Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer, Heidelberg (1992)

    Google Scholar 

  22. McMillan, K.L.: Interpolation and SAT-Based Model Checking. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 1–13. Springer, Heidelberg (2003)

    Google Scholar 

  23. McMillan, K.L.: Lazy Abstraction with Interpolants. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 123–136. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  24. McMillan, K.L., Amla, N.: Automatic Abstraction without Counterexamples. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 2–17. Springer, Heidelberg (2003)

    Google Scholar 

  25. Pike, L.: Real-time system verification by k-induction. Technical Report TM-2005-213751, NASA Langley Research Center (May 2005)

    Google Scholar 

  26. Queille, J.-P., Sifakis, J.: Specification and verification of concurrent systems in CESAR. In: Dezani-Ciancaglini, M., Montanari, U. (eds.) Programming 1982. LNCS, vol. 137, pp. 337–351. Springer, Heidelberg (1982)

    Google Scholar 

  27. Sheeran, M., Singh, S., Stålmarck, G.: Checking Safety Properties Using Induction and a SAT-Solver. In: Johnson, S.D., Hunt Jr., W.A. (eds.) FMCAD 2000. LNCS, vol. 1954, pp. 108–125. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  28. Vardi, M.Y., Wolper, P.: An Automata-Theoretic Approach to Automatic Program Verification. In: LICS, pp. 332–344 (1986)

    Google Scholar 

  29. Wang, C., Kim, H., Gupta, A.: Hybrid CEGAR: combining variable hiding and predicate abstraction. In: ICCAD, pp. 310–317 (2007)

    Google Scholar 

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Author information

Authors and Affiliations

  1. FBK-Irst,  

    Stefano Tonetta

Authors
  1. Stefano Tonetta
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Heslington, University of York, Y010 5DD, York, UK

    Ana Cavalcanti

  2. Bell Laboratories, 600 Mountain Ave., 07974, Murray Hill, NY, USA

    Dennis R. Dams

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Tonetta, S. (2009). Abstract Model Checking without Computing the Abstraction. In: Cavalcanti, A., Dams, D.R. (eds) FM 2009: Formal Methods. FM 2009. Lecture Notes in Computer Science, vol 5850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05089-3_7

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  • DOI: https://doi.org/10.1007/978-3-642-05089-3_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05088-6

  • Online ISBN: 978-3-642-05089-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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