Abstract
Counterexample- and proof-based refinement are complementary approaches to iterative abstraction. In the former case, a single abstract counterexample is eliminated by each refinement step, while in the latter case, all counterexamples of a given length are eliminated. In counterexample-based abstraction, the concretization and refinement problems are relatively easy, but the number of iterations tends to be large. Proof-based abstraction, on the other hand, puts a greater burden on the refinement step, which can then become the performance bottleneck. In this paper, we show that counterexample- and proof-based refinement are extremes of a continuum, and propose a hybrid approach that balances the cost and quality of refinement. In a study of a large number of industrial verification problems, we find that there is a strong relation between the effort applied in the refinement phase and the number of refinement iterations. For this reason, proof-based abstraction is substantially more efficient than counterexample-based abstraction. However, a judicious application of the hybrid approach can lessen the refinement effort without unduly increasing the number of iterations, yielding a method that is somewhat more robust overall.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Balarin, F., Sangiovanni-Vincentelli, A.: An iterative approach to language containment. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 29–40. Springer, Heidelberg (1993)
Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, J.: Symbolic model checking: 1020 states and beyond. In: LICS (June 1990)
Chauhan, P., Clarke, E., Kukula, J., Sapra, S., Veith, H., Wang, D.: Automated abstraction refinement for model checking large state spaces using sat based conflict analysis. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, Springer, Heidelberg (2002)
Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Computer Aided Verification, pp. 154–169 (2000)
Clarke, E.M., Gupta, A., Kukula, J., Strichman, O.: SAT based abstractionrefinement using ILP and machine learning techniques. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, p. 265. Springer, Heidelberg (2002)
Glusman, M., Kamhi, G., Mador-Haim, S., Fraer, R., Vardi, M.Y.: Multiplecounterexample guided iterative abstraction refinement. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 176–191. Springer, Heidelberg (2003)
Govindaraju, S.G., Dill, D.L.: Counterexample-Guided choice of projections in approximate symbolic model checking. In: ICCAD (2000)
Gupta, A., Ganai, M., Yang, Z., Ashar, P.: Iterative abstraction using sat-based bmc with proof analysis. In: ICCAD (2003)
Kupferman, O., Vardi, M.Y.: Model checking of safety properties. Formal Methods in System Design 19(3), 291–314 (2001)
Kurshan, R.P.: Computer-Aided-Verification of Coordinating Processes. Princeton University Press, Princeton (1994)
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)
Moskewicz, M.W., Madigan, C.F.,, Y.Z.L.Z., Malik, S.: Chaff: Engineering an efficient SAT solver. In: Design Automation Conference, pp. 530–535 (2001)
Pnueli, A., Lichtenstein, O.: Checking that finite state concurrent programs satisfy their linear specification. In: POPL (1985)
Silva, J.P.M., Sakallah, K.A.: GRASP–a new search algorithm for satisfiability. In: ICCAD (1996)
Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: Logic in Computer Science (LICS 1986), pp. 322–331 (1986)
Wang, C., Li, B., Jin, H., Hachtel, G., Somenzi, F.: Improving ariadne’s bundle by following multiple threads in abstraction refinement. In: ICCAD (2003)
Wang, D., Ho, P., Long, J., Kukula, J.H., Zhu, Y., Tony Ma, H., Damiano, R.: Formal property verification by abstraction refinement with formal, simulation and hybrid engines. In: Design Automation Conference, pp. 35–40 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Amla, N., McMillan, K.L. (2004). A Hybrid of Counterexample-Based and Proof-Based Abstraction. In: Hu, A.J., Martin, A.K. (eds) Formal Methods in Computer-Aided Design. FMCAD 2004. Lecture Notes in Computer Science, vol 3312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30494-4_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-30494-4_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23738-9
Online ISBN: 978-3-540-30494-4
eBook Packages: Springer Book Archive