Advertisement

Mapping Problems with Finite-Domain Variables to Problems with Boolean Variables

  • Carlos Ansótegui
  • Felip Manyà
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3542)

Abstract

We define a collection of mappings that transform many-valued clausal forms into satisfiability equivalent Boolean clausal forms, analyze their complexity and evaluate them empirically on a set of benchmarks with state-of-the-art SAT solvers. Our results provide empirical evidence that encoding combinatorial problems with the mappings defined here can lead to substantial performance improvements in complete SAT solvers.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alsinet, T., Béjar, R., Cabiscol, A., Fernández, C., Manyà, F.: Minimal and redundant SAT encodings for the all-interval-series problem. In: Escrig, M.T., Toledo, F.J., Golobardes, E. (eds.) CCIA 2002. LNCS (LNAI), vol. 2504, pp. 139–144. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Ansótegui, C., Béjar, R., Cabiscol, A., Li, C.M., Manyà, F.: Resolution methods for many-valued CNF formulas. In: Fifth International Symposium on the Theory and Applications of Satisfiability Testing, SAT 2002, Cincinnati, USA, pp. 156–163 (2002)Google Scholar
  3. 3.
    Ansótegui, C., Larrubia, J., Li, C.M., Manyà, F.: Mv-Satz: A SAT solver for many-valued clausal forms. In: 4th International Conference Journées de L’Informatique Messine, JIM 2003, Metz, France (2003)Google Scholar
  4. 4.
    Ansótegui, C., Larrubia, J., Manyà, F.: Boosting Chaff’s performance by incorporating CSP heuristics. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 96–107. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Ansótegui, C., Manyà, F., Béjar, R., Gomes, C.: Solving many-valued SAT encodings with local search. In: Proceedings of the Workshop on Probabilistics Approaches in Search, 18th National Conference on Artificial Intelligence, AAAI 2002, Edmonton, Canada (2002)Google Scholar
  6. 6.
    Baaz, M., Fermüller, C.G.: Resolution-based theorem proving for many-valued logics. Journal of Symbolic Computation 19, 353–391 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Beckert, B., Hähnle, R., Manyà, F.: Transformations between signed and classical clause logic. In: Proceedings, International Symposium on Multiple-Valued Logics, ISMVL 1999, Freiburg, Germany, pp. 248–255. IEEE Press, Los Alamitos (1999)Google Scholar
  8. 8.
    Beckert, B., Hähnle, R., Manyà, F.: The SAT problem of signed CNF formulas. In: Basin, D., D’Agostino, M., Gabbay, D., Matthews, S., Viganò, L. (eds.) Labelled Deduction. Applied Logic Series, vol. 17, pp. 61–82. Kluwer, Dordrecht (2000)Google Scholar
  9. 9.
    Béjar, R., Cabiscol, A., Fernández, C., Manyà, F., Gomes, C.P.: Capturing structure with satisfiability. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 137–152. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Béjar, R., Hähnle, R., Manyà, F.: A modular reduction of regular logic to classical logic. In: Proceedings, 31st International Symposium on Multiple-Valued Logics (ISMVL), Warsaw, Poland, pp. 221–226. IEEE CS Press, Los Alamitos (2001)CrossRefGoogle Scholar
  11. 11.
    Béjar, R., Manyà, F.: A comparison of systematic and local search algorithms for regular CNF formulas. In: Hunter, A., Parsons, S. (eds.) ECSQARU 1999. LNCS (LNAI), vol. 1638, pp. 22–31. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  12. 12.
    Culberson, J.: Graph coloring page: The flat graph generator (1995) See, http://web.cs.ualberta.ca/~joe/Coloring/Generators/flat.html
  13. 13.
    Escalada-Imaz, G., Manyà, F.: The satisfiability problem for multiple-valued Horn formulæ. In: Proceedings, International Symposium on Multiple-Valued Logics, ISMVL1994, Boston/MA, USA, pp. 250–256. IEEE Press, Los Alamitos (1994)Google Scholar
  14. 14.
    Frisch, A.M., Peugniez, T.J.: Solving non-boolean satisfiability problems with stochastic local search. In: Proceedings of the International Joint Conference on Artificial Intelligence, IJCAI 2001, pp. 282–288 (2001)Google Scholar
  15. 15.
    Hähnle, R.: Towards an efficient tableau proof procedure for multiple-valued logics. In: Schönfeld, W., Börger, E., Kleine Büning, H., Richter, M.M. (eds.) CSL 1990. LNCS, vol. 533, pp. 248–260. Springer, Heidelberg (1991)Google Scholar
  16. 16.
    Hähnle, R.: Automated Deduction in Multiple-Valued Logics. In: International Series of Monographs in Computer Science, vol. 10. Oxford University Press, Oxford (1994)Google Scholar
  17. 17.
    Hähnle, R.: Advanced many-valued logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 2. Kluwer, Dordrecht (2001)Google Scholar
  18. 18.
    Manyà, F.: Proof Procedures for Multiple-Valued Propositional Logics. PhD thesis, Universitat Autònoma de Barcelona (1996)Google Scholar
  19. 19.
    Manyà, F.: The 2-SAT problem in signed CNF formulas. Multiple-Valued Logic. An International Journal 5(4), 307–325 (2000)zbMATHMathSciNetGoogle Scholar
  20. 20.
    Manyà, F., Béjar, R., Escalada-Imaz, G.: The satisfiability problem in regular CNF-formulas. Soft Computing: A Fusion of Foundations, Methodologies and Applications 2(3), 116–123 (1998)CrossRefGoogle Scholar
  21. 21.
    Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient sat solver. In: 39th Design Automation Conference (2001)Google Scholar
  22. 22.
    Murray, N.V., Rosenthal, E.: Resolution and path-dissolution in multiple-valued logics. In: Raś, Z.W., Zemankova, M. (eds.) ISMIS 1991. LNCS (LNAI), vol. 542, pp. 570–579. Springer, Heidelberg (1991)Google Scholar
  23. 23.
    Prestwich, S.D.: Local search on SAT-encoded colouring problems. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 105–109. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  24. 24.
    Smith, B., Dyer, M.: Locating the phase transition in binary constraint satisfaction problems. Artificial Intelligence 81, 155–181 (1996)CrossRefMathSciNetGoogle Scholar
  25. 25.
    Walsh, T.: SAT v CSP. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 441–456. Springer, Heidelberg (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Carlos Ansótegui
    • 1
  • Felip Manyà
    • 1
  1. 1.Computer Science DepartmentUniversitat de LleidaLleidaSpain

Personalised recommendations