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A Compressing Translation from Propositional Resolution to Natural Deduction

  • Hasan Amjad
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4720)

Abstract

We describe a translation from SAT solver generated propositional resolution refutation proofs to classical natural deduction proofs. The resulting proof can usually be checked quicker than one that simply simulates the original resolution proof. We use this result in interactive theorem provers, to speed up reconstruction of SAT solver generated proofs. The translation is efficient, running in time linear in the length of the original proof, and effective, easily scaling up to large proofs with millions of inferences.

Keywords

Conjunctive Normal Form Natural Deduction Path Label Resolution Proof Interactive Theorem Prover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alekhnovich, M., Razborov, A.A.: Resolution is not automatizable unless W[P] is tractable. In: FOCS, pp. 210–219. IEEE Computer Society Press, Los Alamitos (2001)Google Scholar
  2. 2.
    Fontaine, P., Marion, J.-Y., Merz, S., Nieto, L.P., Tiu, A.F.: Expressiveness + automation + soundness: Towards combining SMT solvers and interactive proof assistants. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006 and ETAPS 2006. LNCS, vol. 3920, pp. 167–181. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Gordon, M.J.C., Melham, T.F.: Introduction to HOL: A theorem-proving environment for higher order logic. Cambridge University Press, Cambridge (1993)zbMATHGoogle Scholar
  4. 4.
    Harrison, J.: Metatheory and reflection in theorem proving: A survey and critique. Technical Report CRC-053, SRI International (1995)Google Scholar
  5. 5.
    Harrison, J.: HOL Light: A tutorial introduction. In: Srivas, M., Camilleri, A. (eds.) FMCAD 1996. LNCS, vol. 1166, pp. 265–269. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  6. 6.
    Harrison, J.: Stålmarck’s algorithm as a HOL derived rule. In: von Wright, J., Grundy, J., Harrison, J. (eds.) TPHOLs 1996. LNCS, vol. 1125, pp. 221–234. Springer, Heidelberg (1996)Google Scholar
  7. 7.
    Huet, G., Kahn, G., Paulin-Mohring, C.: The Coq proof assistant: A tutorial: Version 7.2. Technical Report RT-0256, INRIA (February 2002)Google Scholar
  8. 8.
    Mitchell, D.G.: A SAT solver primer. In: EATCS Bulletin (The Logic in Computer Science Column), vol. 85, pp. 112–133 (February 2005)Google Scholar
  9. 9.
    Morrison, D.R.: PATRICIA-Practical Algorithm To Retrieve Information Code. In Alphanumeric. J. ACM 15(4), 514–534 (1968)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: Proceedings of the 38th Design Automation Conference, pp. 530–535. ACM Press, New York (2001)Google Scholar
  11. 11.
    Owre, S., Rushby, J.M., Shankar, N.: PVS: A prototype verification system. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 748–752. Springer, Heidelberg (1992)Google Scholar
  12. 12.
    Paulson, L.C.: A Generic Theorem Prover. In: Paulson, L.C. (ed.) Isabelle. LNCS, vol. 828, Springer, Heidelberg (1994)Google Scholar
  13. 13.
    Shankar, N.: Using decision procedures with a higher-order logic. In: Boulton, R.J., Jackson, P.B. (eds.) TPHOLs 2001. LNCS, vol. 2152, pp. 5–26. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Sinz, C.: Compressing propositional proofs by common subproof extraction. In: Pichler, F. (ed.) Euro Conference on Computer Aided Systems Theory (2007)Google Scholar
  15. 15.
    Ukkonen, E.: Online construction of suffix trees. Algorithmica 14(3), 249–260 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Weber, T., Amjad, H.: Efficiently checking propositional refutations in HOL theorem provers.JAL (special issue on Empirically Successful Computerized Reasoning) (to appear, 2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Hasan Amjad
    • 1
  1. 1.University of Cambridge Computer Laboratory, William Gates Building, 15 JJ Thomson Avenue, Cambridge CB3 0FDUK

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