SAT Based Abstraction-Refinement Using ILP and Machine Learning Techniques

  • Edmund Clarke
  • Anubhav Gupta
  • James Kukula
  • Ofer Strichman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2404)


We describe new techniques for model checking in the counterexample guided abstraction/refinement framework. The abstraction phase ‘hides’ the logic of various variables, hence considering them as inputs. This type of abstraction may lead to ‘spurious’ counterexamples, i.e. traces that can not be simulated on the original (concrete) machine. We check whether a counterexample is real or spurious with a SAT checker. We then use a combination of Integer Linear Programming (ILP) and machine learning techniques for refining the abstraction based on the counterexample. The process is repeated until either a real counterexample is found or the property is verified. We have implemented these techniques on top of the model checker NuSMV and the SAT solver Chaff. Experimental results prove the viability of these new techniques.


Model Check Integer Linear Program Visible Variable Concrete System Integer Linear Program Problem 
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.
    F. Balarin and A. Sangiovanni-Vinventelli. An iterative approah to language containment. In C. Courcoubetis, editor, Proc. 5 th Intl. Conference on Computer Aided Verification (CAV’94), volume 697 of Lect. Notes in Comp. Sci., pages 29–40. Springer-Verlag, 1993.Google Scholar
  2. 2.
    M. Berkelaar. lpsolve, version 2.0. Eindhoven Univ. Tech., The Netherlands.Google Scholar
  3. 3.
    A. Biere, A. Cimatti, E. Clarke, and Y. Zhu. Symbolic model checking without BDDs. In Proc. of the Workshop on Tools and Algorithms for the Construction and Analysis of Systems (TACAS’99), LNCS. Springer-Verlag, 1999.Google Scholar
  4. 4.
    A. Cimatti, E. Clarke, F. Giunchiglia, and M. Roveri. NuSMV: a new symbolic model checker. Int. Journal of Software Tools for Technology Transfer (STTT), 1998.Google Scholar
  5. 5.
    E. Clarke, O. Grumberg, S. Jha, Y. Lu, and H. Veith. Counterexample-guided abstraction refinement. In E. A. Emerson and A. P. Sistla, editors, Proc. 12th Intl. Conference on Computer Aided Verification (CAV’00), volume 1855 of Lect. Notes in Comp. Sci. Springer-Verlag, 2000.Google Scholar
  6. 6.
    E. M. Clarke, O. Grumberg, and D. E. Long. Model checking and abstraction. ACM Trans. Prog. Lang. Sys., 16(5):1512–1542, 1994.CrossRefGoogle Scholar
  7. 7.
    Satyaki Das and David L. Dill. Successive approximation of abstract transition relations. In Proceedings of the Sixteenth Annual IEEE Symposium on Logic in Computer Science, 2001. June 2001, Boston, USA.Google Scholar
  8. 8.
    R. Kurshan. Computer aided verification of coordinating processes. Princeton University Press, 1994.Google Scholar
  9. 9.
    J. Lind-Nielsen and H. Andersan. Stepwise CTL model checking of state/event systems. In N. Halbwachs and D. Peled, editors, Proc. 11th Intl. Conference on Computer Aided Verification (CAV’99), volume 1633 of Lect. Notes in Comp. Sci., pages 316–327. Springer-Verlag, 1999.Google Scholar
  10. 10.
    Tom M. Mitchell. Machine Learning. WCB/McGraw-Hill, 1997.Google Scholar
  11. 11.
    M. Moskewicz, C. Madigan, Y. Zhao, L. Zhang, and S. Malik. Chaff: Engineering an efficient SAT solver. In Proc. Design Automation Conference 2001 (DAC’01), 2001.Google Scholar
  12. 12.
    J. R. Quinlan. Induction of decision trees. Machine Learning, 1986.Google Scholar
  13. 13.
    J. R. Quinlan. C4.5: Programs for Machine Learning. Morgan Kaufmann, San Mateo, CA, 1993.Google Scholar
  14. 14.
    Dong Wang, Pei-Hsin Ho, Jiang Long, James Kukula, Yunshan Zhu, Tony Ma, and Robert Damiano. Formal property verification by abstraction refinement with formal, simulation and hybrid engines. In Proc. Design Automation Conference 2001 (DAC’01), 2001.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Edmund Clarke
    • 1
  • Anubhav Gupta
    • 1
  • James Kukula
    • 2
  • Ofer Strichman
    • 1
  1. 1.Computer ScienceCarnegie Mellon UniversityPittsburgh
  2. 2.SynopsysBeaverton

Personalised recommendations