Abstract
Counterexample-guided abstraction refinement (CEGAR) is a powerful technique to scale automatic program analysis techniques to large programs. However, so far it has been used primarily for model checking in the context of predicate abstraction. We formalize CEGAR for general powerset domains. If a spurious abstract counterexample needs to be removed through abstraction refinement, there are often several choices, such as which program location(s) to refine, which abstract domain(s) to use at different locations, and which abstract values to compute. We define several plausible preference orderings on abstraction refinements, such as refining as “late” as possible and as “coarse” as possible. We present generic algorithms for finding refinements that are optimal with respect to the different preference orderings. We also compare the different orderings with respect to desirable properties, including the property if locally optimal refinements compose to a global optimum. Finally, we point out some difficulties with CEGAR for non-powerset domains.
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
Ball, T., Rajamani, S.K.: The slam project: Debugging system software via static analysis. In: POPL ’02: Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, Portland, Oregon, pp. 1–3. ACM Press, New York (2002)
Beyer, D., Henzinger, T.A., Théoduloz, G.: Lazy shape analysis. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 532–546. Springer, Heidelberg (2006)
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)
Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction of approximation of fixed points. In: Proc. Symp. on Principles of Prog. Languages, pp. 238–252. ACM Press, New York (1977)
Giacobazzi, R., Quintarelli, E.: Incompleteness, counterexamples, and refinements in abstract model-checking. In: Cousot, P. (ed.) SAS 2001. LNCS, vol. 2126, pp. 356–373. Springer, Heidelberg (2001)
Gulavani, B.S., Rajamani, S.K.: Counterexample driven refinement for abstract interpretation. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006 and ETAPS 2006. LNCS, vol. 3920, pp. 474–488. Springer, Heidelberg (2006)
Henzinger, T.A., et al.: Abstractions from proofs. In: POPL ’04: Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages, Venice, Italy, pp. 232–244. ACM Press, New York (2004)
Henzinger, T.A., et al.: Lazy abstraction. In: Symposium on Principles of Programming Languages, pp. 58–70 (2002)
Lev-Ami, T., Sagiv, M.: TVLA: A framework for Kleene based static analysis. In: Palsberg, J. (ed.) SAS 2000. LNCS, vol. 1824, pp. 280–301. Springer, Heidelberg (2000)
Loginov, A., Reps, T., Sagiv, M.: Abstraction refinement via inductive learning. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 519–533. Springer, Heidelberg (2005)
Nielson, F., Nielson, H.R., Hankin, C.: Principles of Program Analysis. Springer, Heidelberg (2001)
Sagiv, M., Reps, T., Wilhelm, R.: Parametric shape analysis via 3-valued logic. ACM Transactions on Programming Languages and Systems (TOPLAS) 24(3), 217–298 (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this chapter
Cite this chapter
Manevich, R., Field, J., Henzinger, T.A., Ramalingam, G., Sagiv, M. (2007). Abstract Counterexample-Based Refinement for Powerset Domains. In: Reps, T., Sagiv, M., Bauer, J. (eds) Program Analysis and Compilation, Theory and Practice. Lecture Notes in Computer Science, vol 4444. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71322-7_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-71322-7_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71315-9
Online ISBN: 978-3-540-71322-7
eBook Packages: Computer ScienceComputer Science (R0)