Interpolant Strength

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5944)


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.


Model Check Conjunctive Normal Form Internal Vertex Labelling Function Initial Vertex 
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  1. 1.
    Andrews, P.B.: Resolution with merging. Journal of the ACM 15(3), 367–381 (1968)zbMATHCrossRefGoogle Scholar
  2. 2.
    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)Google Scholar
  3. 3.
    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)Google Scholar
  4. 4.
    Craig, W.: Linear reasoning. A new form of the Herbrand-Gentzen theorem. Journal of Symbolic Logic 22(3), 250–268 (1957)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    D’Silva, V., Kroening, D., Purandare, M., Weissenbacher, G.: Interpolant strength. Technical Report 652, Institute for Computer Science, ETH Zurich (November 2009)Google Scholar
  6. 6.
    Huang, G.: Constructing Craig interpolation formulas. In: Li, M., Du, D.-Z. (eds.) COCOON 1995. LNCS, vol. 959, pp. 181–190. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  7. 7.
    Jhala, R., McMillan, K.L.: Interpolant-based transition relation approximation. Logical Methods in Computer Science (LMCS) 3(4) (2007)Google Scholar
  8. 8.
    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)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Maehara, S.: On the interpolation theorem of Craig (in Japanese). Sûgaku 12, 235–237 (1961)MathSciNetGoogle Scholar
  10. 10.
    Mancosu, P.: Interpolations. Essays in Honor of William Craig. Synthese, vol. 164:3. Springer, Heidelberg (2008)Google Scholar
  11. 11.
    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)Google Scholar
  12. 12.
    McMillan, K.L.: An interpolating theorem prover. Theoretical Comput. Sci. 345(1), 101–121 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Pudlák, P.: Lower bounds for resolution and cutting plane proofs and monotone computations. The Journal of Symbolic Logic 62(3), 981–998 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    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)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Computing LaboratoryOxford University 
  2. 2.Computer Systems InstituteETH Zurich 

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