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Haifa Verification Conference

HVC 2012: Hardware and Software: Verification and Testing pp 72–85Cite as

Computing Interpolants without Proofs

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7857))

Abstract

We describe an incremental algorithm for computing interpolants for a pair ϕ A , ϕ B of formulas in propositional logic. In contrast with the common approaches, our method does not require a proof of unsatisfiability of ϕ A  ∧ ϕ B , and can be realized using any SAT solver as a black box. We achieve this by combining model enumeration with the ability to easily generate interpolants in the special case that one of the formulas is a cube.

This work is partially supported by the European Community under the call FP7-ICT-2009-5 – project PINCETTE 257647.

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References

  1. Achá, R.J.A., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E.: Practical algorithms for unsatisfiability proof and core generation in SAT solvers. AI Commun. 23(2-3), 145–157 (2010)

    MathSciNet  MATH  Google Scholar 

  2. Brauer, J., King, A., Kriener, J.: Existential quantification as incremental SAT. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 191–207. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  3. Bradley, A.R.: SAT-based model checking without unrolling. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 70–87. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  4. Chambers, B., Manolios, P., Vroon, D.: Faster SAT solving with better CNF generation. In: DATE, pp. 1590–1595 (2009)

    Google Scholar 

  5. Craig, W.: Linear reasoning. A new form of the Herbrand-Gentzen theorem. J. Symb. Log. 22(3), 250–268 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  6. Desrosiers, C., Galinier, P., Hertz, A., Paroz, S.: Using heuristics to find minimal unsatisfiable subformulas in satisfiability problems. J. Comb. Optim. 18(2), 124–150 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Goldberg, E., Manolios, P.: Quantifier elimination by dependency sequents. CoRR, abs/1201.5653 (2012)

    Google Scholar 

  9. Jin, H., Somenzi, F.: Prime clauses for fast enumeration of satisfying assignments to Boolean circuits. In: DAC, pp. 750–753 (2005)

    Google Scholar 

  10. Krajícek, J.: Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic. J. Symb. Log. 62(2), 457–486 (1997)

    Article  MATH  Google Scholar 

  11. Kroening, D., Weissenbacher, G.: Verification and falsification of programs with loops using predicate abstraction. Formal Asp. Comput. 22(2), 105–128 (2010)

    Article  MATH  Google Scholar 

  12. Lee, R.-R., Jiang, J.-H.R., Hung, W.-L.: Bi-decomposing large Boolean functions via interpolation and satisfiability solving. In: DAC, pp. 636–641 (2008)

    Google Scholar 

  13. Lee, C.-C., Jiang, J.-H.R., Huang, C.-Y., Mishchenko, A.: Scalable exploration of functional dependency by interpolation and incremental SAT solving. In: ICCAD, pp. 227–233 (2007)

    Google Scholar 

  14. McMillan, K.L.: Applying SAT methods in unbounded symbolic model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 250–264. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  15. 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)

    Chapter  Google Scholar 

  16. McMillan, K.L.: Applications of Craig interpolants in model checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 1–12. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  17. McMillan, K.L.: Lazy annotation for program testing and verification. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 104–118. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  18. Nadel, A.: Boosting minimal unsatisfiable core extraction. In: FMCAD, pp. 221–229 (2010)

    Google Scholar 

  19. Park, T.J., Van Gelder, A.: Partitioning methods for satisfiability testing on large formulas. Inf. Comput. 162(1-2), 179–184 (2000)

    Article  MATH  Google Scholar 

  20. Pudlák, P.: Lower bounds for resolution and cutting plane proofs and monotone computations. J. Symb. Log. 62(3), 981–998 (1997)

    Article  MATH  Google Scholar 

  21. Sinz, C.: Towards an optimal CNF encoding of Boolean cardinality constraints. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 827–831. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  22. Marques-Silva, J., Lynce, I.: On improving MUS extraction algorithms. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 159–173. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  23. Zhang, L., Malik, S.: Validating SAT solvers using an independent resolution-based checker: Practical implementations and other applications. In: DATE, pp. 10880–10885 (2003)

    Google Scholar 

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Author information

Authors and Affiliations

  1. IBM Research – Haifa, Israel

    Hana Chockler, Alexander Ivrii & Arie Matsliah

Authors
  1. Hana Chockler
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  2. Alexander Ivrii
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  3. Arie Matsliah
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Editor information

Editors and Affiliations

  1. Institute for Formal Models and Verification, Johannes Kepler University, Linz, Austria

    Armin Biere

  2. IBM Research Laboratory, 31905, Haifa, Israel

    Amir Nahir

  3. Universidad Politecnica de Valencia, 46022, Valencia, Spain

    Tanja Vos

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Chockler, H., Ivrii, A., Matsliah, A. (2013). Computing Interpolants without Proofs. In: Biere, A., Nahir, A., Vos, T. (eds) Hardware and Software: Verification and Testing. HVC 2012. Lecture Notes in Computer Science, vol 7857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39611-3_12

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  • DOI: https://doi.org/10.1007/978-3-642-39611-3_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39610-6

  • Online ISBN: 978-3-642-39611-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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