Property-Driven Partitioning for Abstraction Refinement

  • Roberto Sebastiani
  • Stefano Tonetta
  • Moshe Y. Vardi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4424)


Partitioning and abstraction have been studied extensively both in hardware and in software verification. The abstraction is typically partitioned according to the system design in the case of hardware or the control graph in the case of software. In this work we build on previous work on Property-Driven Partitioning (PDP), a hybrid Symbolic Model-Checking (SMC) technique for ω-regular properties in which the state space is partitioned according to the states of the property automaton. We investigate a new paradigm for abstraction refinement in SMC, which combines abstraction and PDP: each PDP partition may contain a different abstraction, so that it can be refined independently from the others; in case of a spurious counterexample π, the system is refined only in those partitions that are necessary to rule out π. We performed a preliminary experimental evaluation comparing standard Counterexample-Guided Abstraction Refinement (CEGAR) with its partitioned counterpart, which confirmed that the partitioned technique always allows for using coarser abstractions. While earlier work has shown that PDP almost always improves the performance of SMC, our experiments here show that this is not always the case for partitioned abstraction refinement, as in some cases the overhead due to the localization of the abstraction is too high.


Model Check Localization Reduction Symbolic Model Check Bound Model Check Concrete 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.
    Clarke, E., et al.: Symbolic Model Checking without BDDs. In: Cleaveland, W.R. (ed.) ETAPS 1999 and TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)Google Scholar
  2. 2.
    Burch, J.R., et al.: Symbolic Model Checking: 1020 States and Beyond. Information and Computation 98(2), 142–170 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Cho, H., et al.: Automatic state space decomposition for approximate FSM traversal based on circuit analysis. IEEE Trans. on CAD of Integrated Circuits and Systems 15(12), 1451–1464 (1996)CrossRefGoogle Scholar
  4. 4.
    Clarke, E., et al.: NUSMV: A New Symbolic Model Verifier. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 495–499. Springer, Heidelberg (1999)Google Scholar
  5. 5.
    Clarke, E.M., et al.: Counterexample-Guided Abstraction Refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  6. 6.
    Clarke, E.M., Grumberg, O., Long, D.E.: Model Checking and Abstraction. ACM Trans. Program. Lang. Syst. 16(5), 1512–1542 (1994)CrossRefGoogle Scholar
  7. 7.
    Clarke, E.M., et al.: 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)CrossRefGoogle Scholar
  8. 8.
    Emerson, E.A., Lei, C.L.: Efficient Model Checking in Fragments of the Propositional μ-Calculus. In: Proceedings of the LICS’86, pp. 267–278 (1986)Google Scholar
  9. 9.
    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
  10. 10.
    Henzinger, T.A., et al.: Abstractions from proofs. In: Proceedings of POPL’04, pp. 232–244 (2004)Google Scholar
  11. 11.
    Henzinger, T.A., et al.: Lazy abstraction. In: Proceedings of POPL’02, pp. 58–70 (2002)Google Scholar
  12. 12.
    Holzmann, G.J.: The SPIN model checker: Primer and reference manual. Addison-Wesley, Reading (2003)Google Scholar
  13. 13.
    Kurshan, R.P.: Computer Aided Verification of Coordinating Processes. Princeton University Press, Princeton (1994)Google Scholar
  14. 14.
    Nguyen, M.D., et al.: Transition-by-Transition FSM Traversal for Reachability Analysis in Bounded Model Checking. In: Proceedings of ICCAD’05 (2005)Google Scholar
  15. 15.
    Sebastiani, R., et al.: GSTE is Partitioned Model Checking. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 229–241. Springer, Heidelberg (2004)Google Scholar
  16. 16.
    Sebastiani, R., Tonetta, S., Vardi, M.Y.: Symbolic Systems, Explicit Properties: On Hybrid Approaches for LTL Symbolic Model Checking. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 350–363. Springer, Heidelberg (2005)Google Scholar
  17. 17.
    Vardi, M.Y., Wolper, P.: An Automata-Theoretic Approach to Automatic Program Verification. In: Proceedings of LICS’86, pp. 332–344. IEEE Computer Society Press, Los Alamitos (1986)Google Scholar
  18. 18.
    Wang, C., et al.: Improving Ariadne’s Bundle by Following Multiple Threads in Abstraction Refinement. In: Proceedings of ICCAD’03, pp. 408–415 (2003)Google Scholar
  19. 19.
    Yang, J., Seger, C.-J.H.: Introduction to Generalized Symbolic Trajectory Evaluation. IEEE Transactions on Very Large Scale Integration Systems 11(3) (2003)Google Scholar
  20. 20.
    Yang, J., Seger, C.-J.H.: Generalized Symbolic Trajectory Evaluation - Abstraction in Action. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 70–87. Springer, Heidelberg (2002)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Roberto Sebastiani
    • 1
  • Stefano Tonetta
    • 2
  • Moshe Y. Vardi
    • 3
  1. 1.DIT, Università di TrentoItaly
  2. 2.University of LuganoSwitzerland
  3. 3.Dept. of Computer Science, Rice UniversityUSA

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