Abstract
Interpolant-based model checking is an approximate method for computing invariants of transition systems. The performance of the model checker is contingent on the approximation computed, which in turn depends on the logical strength of the interpolants. A good approximation is coarse enough to enable rapid convergence but strong enough to be contained within the weakest inductive invariant. We present a system for constructing propositional interpolants of different strength from a resolution refutation. This system subsumes existing methods and allows interpolation systems to be ordered by the logical strength of the obtained interpolants. Interpolants of different strength can also be obtained by transforming a resolution proof. We analyse an existing proof transformation, generalise it, and characterise the interpolants obtained.
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References
Andrews, P.B.: Resolution with merging. Journal of the ACM 15(3), 367–381 (1968)
Bar-Ilan, O., Fuhrmann, O., Hoory, S., Shacham, O., Strichman, O.: Linear-time reductions of resolution proofs. Technical Report IE/IS-2008-02, Technion (2008)
Buss, S.R.: Propositional proof complexity: An introduction. In: Berger, U., Schwichtenberg, H. (eds.) Computational Logic. NATO ASI Series F: Computer and Systems Sciences, vol. 165, pp. 127–178. Springer, Heidelberg (1999)
Craig, W.: Linear reasoning. A new form of the Herbrand-Gentzen theorem. Journal of Symbolic Logic 22(3), 250–268 (1957)
D’Silva, V., Kroening, D., Purandare, M., Weissenbacher, G.: Interpolant strength. Technical Report 652, Institute for Computer Science, ETH Zurich (November 2009)
Huang, G.: Constructing Craig interpolation formulas. In: Li, M., Du, D.-Z. (eds.) COCOON 1995. LNCS, vol. 959, pp. 181–190. Springer, Heidelberg (1995)
Jhala, R., McMillan, K.L.: Interpolant-based transition relation approximation. Logical Methods in Computer Science (LMCS) 3(4) (2007)
Krajíček, J.: Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic. The Journal of Symbolic Logic 62(2), 457–486 (1997)
Maehara, S.: On the interpolation theorem of Craig (in Japanese). Sûgaku 12, 235–237 (1961)
Mancosu, P.: Interpolations. Essays in Honor of William Craig. Synthese, vol. 164:3. Springer, Heidelberg (2008)
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. Theoretical Comput. Sci. 345(1), 101–121 (2005)
Pudlák, P.: Lower bounds for resolution and cutting plane proofs and monotone computations. The Journal of Symbolic Logic 62(3), 981–998 (1997)
Yorsh, G., Musuvathi, M.: A combination method for generating interpolants. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 353–368. Springer, Heidelberg (2005)
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D’Silva, V., Kroening, D., Purandare, M., Weissenbacher, G. (2010). Interpolant Strength. In: Barthe, G., Hermenegildo, M. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2010. Lecture Notes in Computer Science, vol 5944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11319-2_12
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DOI: https://doi.org/10.1007/978-3-642-11319-2_12
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