Advertisement

Applications of Craig Interpolation to Model Checking

  • Kenneth McMillan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3536)

Abstract

A Craig interpolant [1] for a mutually inconsistent pair of formulas (A,B) is a formula that is (1) implied by A, (2) inconsistent with B, and (3) expressed over the common variables of A and B. It is known that a Craig interpolant can be efficiently derived from a refutation of AB, for certain theories and proof systems. For example, interpolants can be derived from resolution proofs in propositional logic, and for systems of linear inequalities over the reals [6,4]. These methods have been recently extended to combine linear inequalities with uninterpreted function symbols, and to deal with integer models [5]. One key aspect of these procedures is that the yield quantifier-free interpolants when the premises A and B are quantifier-free.

References

  1. 1.
    Craig, W.: Linear reasoning: A new form of the Herbrand-Gentzen theorem. J. Symbolic Logic 22(3), 250–268 (1957)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Henzinger, T.A., Jhala, R., Majumdar, R., McMillan, K.L.: Abstractions from proofs. In: ACM Symp. on Principles of Prog. Lang, POPL 2004 (2004) (to appear)Google Scholar
  3. 3.
    Jhala, R., McMillan, K.L.: Interpolant-based transition relation approximation. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. R. Jhala and K. L. McMillan, vol. 3576, pp. 39–51. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Krajíček, J.: Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic. J. Symbolic Logic 62(2), 457–486 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    McMillan, K.L.: An interpolating theorem prover. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 16–30. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Pudlák, P.: Lower bounds for resolution and cutting plane proofs and monotone computations. J. Symbolic Logic 62(2), 981–998 (1997)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Saïdi, H., Graf, S.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Kenneth McMillan
    • 1
  1. 1.Cadence Berkeley Labs 

Personalised recommendations