Abstract
Craig interpolation is a well known method of abstraction successfully used in both hardware and software model checking. The logical strength of interpolants can affect the quality of approximations and consequently the performance of the model checkers. Recently, it was observed that for the same resolution proof a complete lattice of interpolants ordered by strength can be derived. Most state-of-the-art model checking techniques based on interpolation subject the interpolants to constraints that ensure efficient verification as, for example, in transition relation approximation for bounded model checking, counterexample-guided abstraction refinement and function summarization for software update checking. However, in general, these verification-specific constraints are not satisfied by all possible interpolants.
The paper analyzes the restrictions within the lattice of interpolants under which the required constraints are satisfied. This enables investigation of the effect of the strength of interpolants on the particular techniques, while preserving their soundness. As an additional benefit, combination of this result with proof manipulation procedures allows the use of optimized solvers to generate interpolants of different strengths for various model checking techniques.
This work is partially supported by the European Community under the call FP7-ICT-2009-5 — project PINCETTE 257647. The work of the second author was partially supported by the Grant Agency of the Czech Republic project P202/12/P180.
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Beyer, D., Henzinger, T.A., Jhala, R., Majumdar, R.: The Software Model Checker Blast: Applications to Software Engineering. Int. J. STTT 9, 505–525 (2007)
Bruttomesso, R., Rollini, S.F., Sharygina, N., Tsitovich, A.: Flexible Interpolation with Local Proof Transformations. In: ICCAD 2010, pp. 770–777. IEEE (2010)
Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-Guided Abstraction Refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000)
Craig, W.: Three Uses of the Herbrand-Gentzen Theorem in Relating Model Theory and Proof Theory. J. of Symbolic Logic, 269–285 (1957)
D’Silva, V., Kroening, D., Purandare, M., Weissenbacher, G.: Interpolant Strength. In: Barthe, G., Hermenegildo, M. (eds.) VMCAI 2010. LNCS, vol. 5944, pp. 129–145. Springer, Heidelberg (2010)
Heizmann, M., Hoenicke, J., Podelski, A.: Nested Interpolants. In: POPL 2010, pp. 471–482. ACM (2010)
Henzinger, T.A., Jhala, R., Majumdar, R., McMillan, K.L.: Abstractions from Proofs. In: POPL 2004, pp. 232–244. ACM (2004)
Jhala, R., McMillan, K.L.: Interpolant-Based Transition Relation Approximation. Logical Methods in Computer Science 3(4) (2007)
Kroening, D., Weissenbacher, G.: Interpolation-Based Software Verification with Wolverine. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 573–578. Springer, Heidelberg (2011)
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)
McMillan, K.L.: An Interpolating Theorem Prover. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 16–30. Springer, Heidelberg (2004)
McMillan, K.L.: Applications of Craig Interpolants in Model Checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 1–12. Springer, Heidelberg (2005)
McMillan, K.L.: Lazy Abstraction with Interpolants. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 123–136. Springer, Heidelberg (2006)
McMillan, K.L.: Lazy Annotation for Program Testing and Verification. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 104–118. Springer, Heidelberg (2010)
Pudlák, P.: Lower Bounds for Resolution and Cutting Plane Proofs and Monotone Computations. Journal of Symbolic Logic 62(3), 981–998 (1997)
Rollini, S.F., Bruttomesso, R., Sharygina, N.: An Efficient and Flexible Approach to Resolution Proof Reduction. In: Barner, S., Kroening, D., Raz, O. (eds.) HVC 2010. LNCS, vol. 6504, pp. 182–196. Springer, Heidelberg (2010)
Sery, O., Fedyukovich, G., Sharygina, N.: Interpolation-based Function Summaries in Bounded Model Checking. In: HVC 2011. LNCS (2011) (to appear)
Vizel, Y., Grumberg, O.: Interpolation-sequence Based Model Checking. In: FMCAD 2009, pp. 1–8. IEEE (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rollini, S.F., Sery, O., Sharygina, N. (2012). Leveraging Interpolant Strength in Model Checking. In: Madhusudan, P., Seshia, S.A. (eds) Computer Aided Verification. CAV 2012. Lecture Notes in Computer Science, vol 7358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31424-7_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-31424-7_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31423-0
Online ISBN: 978-3-642-31424-7
eBook Packages: Computer ScienceComputer Science (R0)