SAT-Based Compositional Verification Using Lazy Learning

  • Nishant Sinha
  • Edmund Clarke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4590)


A recent approach to automated assume-guarantee reasoning (AGR) for concurrent systems relies on computing environment assumptions for components using the L * algorithm for learning regular languages. While this approach has been investigated extensively for message passing systems, it still remains a challenge to scale the technique to large shared memory systems, mainly because the assumptions have an exponential communication alphabet size. In this paper, we propose a SAT-based methodology that employs both induction and interpolation to implement automated AGR for shared memory systems. The method is based on a new lazy approach to assumption learning, which avoids an explicit enumeration of the exponential alphabet set during learning by using symbolic alphabet clustering and iterative counterexample-driven localized partitioning. Preliminary experimental results on benchmarks in Verilog and SMV are encouraging and show that the approach scales well in practice.


Model Check Regular Language Bound Model Check Membership Query Shared Memory System 
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.


  1. 1.
    Foci: An interpolating prover,
  2. 2.
  3. 3.
    Yices: An smt solver,
  4. 4.
    Alur, R., Madhusudan, P., Nam, W.: Symbolic compositional verification by learning assumptions. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, Springer, Heidelberg (2005)Google Scholar
  5. 5.
    Amla, N.: An analysis of sat-based model checking techniques in an industrial environment. In: Borrione, D., Paul, W. (eds.) CHARME 2005. LNCS, vol. 3725, pp. 254–268. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Angluin, D.: Learning regular sets from queries and counterexamples. Information and Computation 75(2), 87–106 (1987)zbMATHCrossRefGoogle Scholar
  7. 7.
    Barringer, H., Giannakopoulou, D., Pasareanu, C.S.: Proof rules for automated compositional verification. In: SAVCBS (2003)Google Scholar
  8. 8.
    Berg, T., Jonsson, B., Raffelt, H.: Regular inference for state machines with parameters. In: Baresi, L., Heckel, R. (eds.) FASE 2006 and ETAPS 2006. LNCS, vol. 3922, pp. 107–121. Springer, Heidelberg (2006)Google Scholar
  9. 9.
    Biere, A., Cimatti, A., Clarke, E.M., Strichman, O., Zue, Y.: Bounded Model Checking. In: Zelkowitz, M. (ed.) Advances in computers, vol. 58 (2003)Google Scholar
  10. 10.
    Sagar Chaki and Ofer Strichman. Optimized L* for assume-guarantee reasoning. In: TACAS (to appear, 2007)Google Scholar
  11. 11.
    Cobleigh, J., Avrunin, G., Clarke, L.: Breaking up is hard to do: an investigation of decomposition for assume-guarantee reasoning. In: ISSTA, pp. 97–108 (2006)Google Scholar
  12. 12.
    Cobleigh, J.M., Giannakopoulou, D., Pasareanu, C.S.: Learning assumptions for compositional verification. In: Garavel, H., Hatcliff, J. (eds.) ETAPS 2003 and TACAS 2003. LNCS, vol. 2619, Springer, Heidelberg (2003)Google Scholar
  13. 13.
    Dutertre, B., de Moura, L.: A fast linear-arithmetic solver for DPLL(T). In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 81–94. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Eén, N., Sörensson, N.: Temporal induction by incremental sat solving. Electr. Notes Theor. Comput. Sci. 89(4) (2003)Google Scholar
  15. 15.
    Armoni, R., et al.: Sat-based induction for temporal safety properties. Electr. Notes Theor. Comput. Sci. 119(2), 3–16 (2005)CrossRefGoogle Scholar
  16. 16.
    Gheorghiu, M., Giannakopoulou, D., Pasareanu, C.S.: Refining interface alphabets for compositional verification. In: TACAS (to Appear)Google Scholar
  17. 17.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, Massachusetts (1979)zbMATHGoogle Scholar
  18. 18.
    Jones, C.B.: Tentative steps toward a development method for interfering programs. ACM Trans. Program. Lang. Syst. 5(4), 596–619 (1983)zbMATHCrossRefGoogle Scholar
  19. 19.
    Maier, P.: A set-theoretic framework for assume-guarantee reasoning. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 821–834. Springer, Heidelberg (2001)Google Scholar
  20. 20.
    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
  21. 21.
    Misra, J., Chandy, K.M.: Proofs of networks of processes. IEEE Trans. Software Eng. 7(4), 417–426 (1981)CrossRefGoogle Scholar
  22. 22.
    Nam, W., Alur, R.: Learning-based symbolic assume-guarantee reasoning with automatic decomposition. In: Graf, S., Zhang, W. (eds.) ATVA 2006. LNCS, vol. 4218, pp. 170–185. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  23. 23.
    Namjoshi, K.S., Trefler, R.J.: On the completeness of compositional reasoning. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 139–153. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  24. 24.
    Pnueli, A.: In transition from global to modular temporal reasoning about programs. In: Logics and models of concurrent systems, Springer, Heidelberg (1985)Google Scholar
  25. 25.
    Prasad, M.R., Biere, A., Gupta, A.: A survey of recent advances in sat-based formal verification. STTT 7(2), 156–173 (2005)CrossRefGoogle Scholar
  26. 26.
    Rivest, R.L., Schapire, R.E.: Inference of finite automata using homing sequences. In: Inf. Comp. vol. 103(2), pp. 299–347 (1993)Google Scholar
  27. 27.
    Sheeran, M., Singh, S., Stalmarck, 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)Google Scholar
  28. 28.
    Sinha, N., Clarke, E.: SAT-based compositional verification using lazy learning. Technical report CMU-CS-07-109, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA (February 2007)Google Scholar
  29. 29.
    Tinelli, C., Ranise, S.: SMT-LIB: The Satisfiability Modulo Theories Library (2005),

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Nishant Sinha
    • 1
  • Edmund Clarke
    • 1
  1. 1.Carnegie Mellon UniversityUSA

Personalised recommendations