Abstract
Abstract interpretation (AI) is one of the most scalable automated approaches to program verification available today. To achieve efficiency, many steps of the analysis, e.g., joins and widening, lose precision. As a result, AI often produces false alarms, coming from the inability to find a safe inductive invariant even when it exists in a chosen abstract domain.
To tackle this problem, we present Vinta, an iterative algorithm that uses Craig interpolants to refine and guide AI away from false alarms. Vinta is based on a novel refinement strategy that capitalizes on recent advances in SMT and interpolation-based verification to (a) find counterexamples to justify alarms produced by AI, and (b) to strengthen an invariant to exclude alarms that cannot be justified. The refinement process continues until either a safe inductive invariant is computed, a counterexample is found, or resources are exhausted. This strategy allows Vinta to recover precision lost in many AI steps, and even to compute inductive invariants that are inexpressible in the chosen abstract domain (e.g., by adding disjunctions and new terms).
We have implemented Vinta and compared it against top verification tools from the recent software verification competition. Our results show that Vinta outperforms state-of-the-art verification tools.
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
Albarghouthi, A., Gurfinkel, A., Chechik, M.: From Under-Approximations to Over-Approximations and Back. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 157–172. Springer, Heidelberg (2012)
Albarghouthi, A., Gurfinkel, A., Chechik, M.: UFO: A Framework for Abstraction- and Interpolation-Based Software Verification. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 672–678. Springer, Heidelberg (2012)
Bagnara, R., Hill, P.M., Zaffanella, E.: Widening Operators for Powerset Domains. STTT 8(4-5), 449–466 (2006)
Beyer, D.: Competition on Software Verification - (SV-COMP). In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 504–524. Springer, Heidelberg (2012), http://sv-comp.sosy-lab.org/
Beyer, D., Keremoglu, M.E.: CPAchecker: A Tool for Configurable Software Verification. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 184–190. Springer, Heidelberg (2011)
Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic Model Checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)
Bourdoncle, F.: Efficient Chaotic Iteration Strategies with Widenings. In: Bjøcrner, D., Broy, M., Pottosin, I.V. (eds.) Proc. of FMPA 1993. LNCS, vol. 735, pp. 128–141. Springer, Heidelberg (1993)
Craig, W.: Three Uses of the Herbrand-Gentzen Theorem in Relating Model Theory and Proof Theory. J. of Symbolic Logic 22(3), 269–285 (1957)
Gulavani, B., Henzinger, T., Kannan, Y., Nori, A., Rajamani, S.: SYNERGY: A New Algorithm for Property Checking. In: Proc. of FSE 2006, pp. 117–127 (2006)
Gulavani, B.S., Chakraborty, S., Nori, A.V., Rajamani, S.K.: Automatically Refining Abstract Interpretations. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 443–458. Springer, Heidelberg (2008)
Gurfinkel, A., Chaki, S., Sapra, S.: Efficient Predicate Abstraction of Program Summaries. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 131–145. Springer, Heidelberg (2011)
Gurfinkel, A., Chaki, S.: Boxes: A Symbolic Abstract Domain of Boxes. In: Cousot, R., Martel, M. (eds.) SAS 2010. LNCS, vol. 6337, pp. 287–303. Springer, Heidelberg (2010)
Henzinger, T.A., Jhala, R., Majumdar, R., McMillan, K.L.: Abstractions from Proofs. In: Proc. of POPL 2004, pp. 232–244 (2004)
Lattner, C., Adve, V.: LLVM: A Compilation Framework for Lifelong Program Analysis & Transformation. In: Proc. of CGO 2004, pp. 75–88 (2004)
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)
de Moura, L., Bjørner, N.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)
Wang, C., Yang, Z., Gupta, A., Ivančić, F.: Using Counterexamples for Improving the Precision of Reachability Computation with Polyhedra. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 352–365. Springer, Heidelberg (2007)
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
Albarghouthi, A., Gurfinkel, A., Chechik, M. (2012). Craig Interpretation. In: Miné, A., Schmidt, D. (eds) Static Analysis. SAS 2012. Lecture Notes in Computer Science, vol 7460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33125-1_21
Download citation
DOI: https://doi.org/10.1007/978-3-642-33125-1_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33124-4
Online ISBN: 978-3-642-33125-1
eBook Packages: Computer ScienceComputer Science (R0)