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Formal verification of a generic framework to synthesize SAT-provers

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Abstract

We present in this paper an application of the ACL2 system to generate and reason about propositional satisfiability provers. For that purpose, we develop a framework in which we define a generic S AT-prover based on transformation rules, and we formalize this generic framework in the ACL2 logic, carrying out a formal proof of its termination, soundness, and completeness. This generic framework can be instantiated to obtain a number of verified and executable SAT-provers in ACL2, and this instantiation can be done in an automated way. Three instantiations of the generic framework are considered: semantic tableaux, sequent calculus, and Davis-Putnam-Logeman-Loveland methods.

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References

  1. Ben-Ari, M:Mathematical Logic for Computer Science, Springer-Verlag, 2001.

  2. Boyer, R. S. and Moore, J S.:A Computational Logic, Academic Press, 1979.

  3. Boyer, R. S. and Moore, J S.: Single-threaded objects in ACL2, inPractical Aspects of Declarative Languages, LNCS 2257, Springer-Verlag, 2002, pp. 9–27.

  4. Caldwell, J.: Classical prepositional decidability via Nuprl proof extraction, inProceedings of the 11th International Conference on Theorem Proving in Higher Order Logics (TPHOLs ′98), LNCS 1479, Springer-Verlag, 1998, pp. 105–122.

  5. Davis, M. and Putnam, H.: A computing procedure for quantification theory,J. Assoc. Comput. Much. 7(3) (1960), 201–215.

    MATH  MathSciNet  Google Scholar 

  6. Davis, M., Logemann, G. and Loveland, D.: A machine program for theorem-proving,Comm. Assoc. Comput. Much. 5(7) (1962), 394–397.

    MathSciNet  Google Scholar 

  7. Dershowitz, N. and Manna, Z.: Proving termination with multiset orderings, inProceedings of the Sixth International Colloquium on Automata, Languages and Programming, LNCS 71, Springer-Verlag, 1979, pp. 188–202.

  8. Fitting, M. C:First-Order Logic and Automated Theorem Proving, Springer-Verlag, 1996.

  9. Gu, J., Purdom, P. W., Franco, J. and Wah, B. W.: Algorithms for the satisfiability (SAT) problem: A survey, inSatisfiability Problem: Theory and Applications, DIMACS: Series in Descrete and Applied Mathematics and Computer Science 35, Amer. Math. Soc, 1997.

  10. Gallier, J. H.:Logic for Computer Science, Foundations of Automatic Theorem Proving, Harper and Row Publishers, 1986.

  11. Kaufmann, M., Manolios, P. and Moore, J S.:Computer-Aided Reasoning: An Approach, Kluwer Academic Publishers, 2000.

  12. Kaufmann, M. and Moore, J S.:ACL2 Version 2.7, 2001. Homepage: http://www.es. utexas.edu/users/moore/acl2/

  13. Kaufmann, M. and Moore, J S.: Structured theory development for a mechanized logic,J. Automated Reasoning 26(2) (2001), 161–203.

    Article  MATH  MathSciNet  Google Scholar 

  14. Martin-Mateos, F. J., Alonso, J. A., Hidalgo, M. J. and Ruiz-Reina, J. L.: A generic instantiation tool and a case study: A generic multiset theory. Presented at 3rd Intl. Workshop on the ACL2 Theorem Prover and Its Applications, Grenoble, 2002.

  15. Martin-Mateos, F. J., Alonso, J. A., Hidalgo, M. J. and Ruiz-Reina, J. L.: Verification in ACL2 of a generic framework to synthesize SAT-provers, inLogic Based Program Synthesis and Tranformation, LNCS 2664, Springer-Verlag, 2003.

  16. Martin-Mateos, F. J., Alonso, J. A., Hidalgo, M. J. and Ruiz-Reina, J. L.: A generic framework for SAT-provers (formalization in ACL2). http: / /www. cs .us. es/clg/theories/ acl2/gen-sat

  17. Ruiz-Reina, J. L., Alonso, J. A., Hidalgo, M. J. and Martin, F. J.: Termination in ACL2 using multiset relation, inThirty Five Years of Automating Mathematics, Applied Logic Series 28, Kluwer Academic Publishers, 2003.

  18. Shankar, N.: Little engines of proof, inFME 2002: Formal Methods — Getting IT Right, LNCS 2391, Springer-Verlag, 2002.

  19. Smullyan, R. M.:First-Order Logic, Springer-Verlag, 1968.

  20. Zhang, H. and Stickel, M. E.: Implementing the Davis-Putnam method,J. Automated Reasoning 24(1–2) (2000), 277–296.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Computational Logic Group, Dept. of Computer Science and Artificial Intelligence, University of Seville, E.T.S.I. Informática, Avda. Reina Mercedes, s/n., 41012, Sevilla, Spain

    Francisco -Jesús Martín-Mateos, José -Antonio Alonso, María -José Hidalgo & José -Luis Ruiz-Reina

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  1. Francisco -Jesús Martín-Mateos
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  2. José -Antonio Alonso
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  3. María -José Hidalgo
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  4. José -Luis Ruiz-Reina
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Corresponding author

Correspondence to Francisco -Jesús Martín-Mateos.

Additional information

This work has been supported by project TIC2000-1368-C03-02 (Ministry of Science and Technology, Spain), cofinanced by FEDER funds.

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Martín-Mateos, F.J., Alonso, J.A., Hidalgo, M.J. et al. Formal verification of a generic framework to synthesize SAT-provers. J Autom Reasoning 32, 287 (2004). https://doi.org/10.1007/BF03177742

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