Abstract
Model checking using Craig interpolants provides an effective method for computing an over-approximation of the set of reachable states using a SAT solver. This method requires proofs of unsatisfiability from the SAT solver to progress. If an over-approximation leads to a satisfiable formula, the computation restarts using more constraints and the previously computed approximation is not reused. Though the new formula eliminates spurious counterexamples of a certain length, there is no guarantee that the subsequent approximation is better than the one previously computed. We take an abstract, approximation-oriented view of interpolation based model checking. We study counterexample-free approximations, which are neither over- nor under-approximations of the set of reachable states but still contain enough information to conclude if counterexamples exist. Using such approximations, we devise a model checking algorithm for approximation refinement and discuss a preliminary implementation of this technique on some hardware benchmarks.
This research is supported by SRC contract 2006-TJ-1539 and a DAC graduate fellowship.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching-time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982)
KrajĂcek, J.: Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic. Journal of Symbolic Logic 62, 457–486 (1997)
Pudlák, P.: Lower bounds for resolution and cutting plane proofs and monotone computations. Journal of Symbolic Logic 62, 981–998 (1997)
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)
Marques-Silva, J.: Interpolant learning and reuse in SAT-based model checking. Electron. Notes Theor. Comput. Sci. 174, 31–43 (2007)
Marques-Silva, J.: Improvements to the Implementation of Interpolant-Based Model Checking. In: Borrione, D., Paul, W. (eds.) CHARME 2005. LNCS, vol. 3725, pp. 367–370. Springer, Heidelberg (2005)
Jhala, R., McMillan, K.L.: Interpolant-based transition relation approximation (2007)
Govindaraju, S.G., Dill, D.L.: Verification by approximate forward and backward reachability. In: International Conference on Computer-Aided Design (ICCAD), pp. 366–370. ACM Press, New York (1998)
Cabodi, G., Nocco, S., Quer, S.: Mixing forward and backward traversals in guided-prioritized BDD-based verification. In: Computer Aided Verification (CAV), Springer, pp. 471–484. Springer, Heidelberg (2002)
Stangier, C., Sidle, T.: Invariant Checking Combining Forward and Backward Traversal. In: Hu, A.J., Martin, A.K. (eds.) FMCAD 2004. LNCS, vol. 3312, pp. 414–429. Springer, Heidelberg (2004)
Cousot, P., Cousot, R.: Refining model checking by abstract interpretation. Automated Software Engineering 6, 69–95 (1999)
Cousot, P., Ganty, P., Raskin, J.F.: Fixpoint-guided abstraction refinements. In: Symposium on Static Analysis (SAS), pp. 333–348. Springer, Heidelberg (2007)
Henzinger, T.A., Kupferman, O., Qadeer, S.: From Pre-historic to Post-modern symbolic model checking. Formal Methods in System Design 23, 303–327 (2003)
Massé, D.: Combining Forward and Backward Analyses of Temporal Properties. In: Danvy, O., Filinski, A. (eds.) PADO 2001. LNCS, vol. 2053, pp. 155–172. Springer, Heidelberg (2001)
Cabodi, G., et al.: Stepping forward with interpolants in unbounded model checking. In: International conference on Computer-aided design (ICCAD), pp. 772–778. ACM Press, New York (2006)
Somenzi, F., Li, B.: Efficient Abstraction Refinement in Interpolation-Based Unbounded Model Checking. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006 and ETAPS 2006. LNCS, vol. 3920, pp. 227–241. Springer, Heidelberg (2006)
Craig, W.: Linear reasoning. A new form of the Herbrand-Gentzen theorem 22, 250–268 (1957)
Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Principles of Programming Languages (POPL), pp. 238–252. ACM Press, New York (1977)
Cousot, P.: Semantic foundations of program analysis. In: Program Flow Analysis: Theory and Applications, pp. 303–342. Prentice-Hall, Englewood Cliffs (1981)
Sheeran, M., Singh, S., Stalmarck, G.: Checking safety properties using induction and a SAT-solver. In: Formal Methods in Computer-Aided Design (FMCAD), pp. 108–125. Springer, Heidelberg (2000)
Bradley, A., Manna, Z.: Checking safety by inductive generalization of counterexamples to induction. In: Formal Methods in Computer-Aided Design (FMCAD), IEEE, Los Alamitos (to appear, 2007)
Corno, F., Reorda, M.S., Squillero, G.: RT-level ITC’99 benchmarks and first ATPG results. IEEE Design and Test 17, 44–53 (2000)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
D’Silva, V., Purandare, M., Kroening, D. (2008). Approximation Refinement for Interpolation-Based Model Checking. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2008. Lecture Notes in Computer Science, vol 4905. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78163-9_10
Download citation
DOI: https://doi.org/10.1007/978-3-540-78163-9_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78162-2
Online ISBN: 978-3-540-78163-9
eBook Packages: Computer ScienceComputer Science (R0)