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Answer Set Solver Backdoors

  • Emilia Oikarinen
  • Matti Järvisalo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8761)

Abstract

Backdoor variables offer a generic notion for providing insights to the surprising success of constraint satisfaction solvers in solving remarkably complex real-world instances of combinatorial problems. We study backdoors in the context of answer set programming (ASP), and focus on studying the relative size of backdoors in terms of different state-of-the-art answer set solving algorithms. We show separations of ASP solver families in terms of the smallest existing backdoor sets for the solvers.

Keywords

Logic Program Unit Propagation Truth Assignment Satisfying Assignment Loop Formula 
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.
    Alviano, M., Dodaro, C., Faber, W., Leone, N., Ricca, F.: WASP: A native ASP solver based on constraint learning. In: Cabalar, P., Son, T.C. (eds.) LPNMR 2013. LNCS (LNAI), vol. 8148, pp. 54–66. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  2. 2.
    Anger, C., Gebser, M., Linke, T., Neumann, A., Schaub, T.: The nomore++ system. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS (LNAI), vol. 3662, pp. 422–426. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press (2009)Google Scholar
  4. 4.
    Brewka, G., Eiter, T., Truszczynski, M.: Answer set programming at a glance. Commun. ACM 54(12), 92–103 (2011)CrossRefGoogle Scholar
  5. 5.
    Clark, K.: Negation as failure. In: Readings in Nonmonotonic Reasoning, pp. 311–325. Morgan Kaufmann Publishers (1987)Google Scholar
  6. 6.
    Darwiche, A., Pipatsrisawat, K.: Complete algorithms. In: Biere et al [3], pp. 99–130Google Scholar
  7. 7.
    Davis, M., Logemann, G., Loveland, D.: A machine program for theorem proving. Communications of the ACM 5(7), 394–397 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of the ACM 7(3), 201–215 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Dilkina, B.N., Gomes, C.P., Malitsky, Y., Sabharwal, A., Sellmann, M.: Backdoors to combinatorial optimization: Feasibility and optimality. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 56–70. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Dilkina, B.N., Gomes, C.P., Sabharwal, A.: Tradeoffs in the complexity of backdoors to satisfiability: Dynamic sub-solvers and learning during search. Ann. Math. Artif. Intell. 70(4), 399–431 (2014)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Erdem, E., Lifschitz, V.: Tight logic programs. Theory and Practice of Logic Programming 3(4-5), 499–518 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Fages, F.: Consistency of Clark’s completion and existence of stable models. Journal of Methods of Logic in Computer Science 1, 51–60 (1994)Google Scholar
  13. 13.
    Fichte, J.K., Szeider, S.: Backdoors to normality for disjunctive logic programs. In: Proc. AAAI. AAAI Press (2013)Google Scholar
  14. 14.
    Gebser, M., Schaub, T.: Characterizing ASP inferences by unit propagation. In: ICLP Workshop on Search and Logic: Answer Set Programming and SAT, Seattle, pp. 41–56 (August 16, 2006)Google Scholar
  15. 15.
    Gebser, M., Kaufmann, B., Schaub, T.: Conflict-driven answer set solving: From theory to practice. Artif. Intell. 187, 52–89 (2012)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Gebser, M., Schaub, T.: Tableau calculi for logic programs under answer set semantics. ACM Trans. Comput. Log. 14(2), 15 (2013)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proc. ICLP/SLP 1988, pp. 1070–1080. MIT Press (1988)Google Scholar
  18. 18.
    Giunchiglia, E., Leone, N., Maratea, M.: On the relation among answer set solvers. Ann. Math. Artif. Intell. 53(1-4), 169–204 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Giunchiglia, E., Lierler, Y., Maratea, M.: Answer set programming based on propositional satisfiability. Journal of Automated Reasoning 36(4), 345–377 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Järvisalo, M., Oikarinen, E.: Extended ASP tableaux and rule redundancy in normal logic programs. Theory and Practice of Logic Programming 8(5-6), 691–716 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV system for knowledge representation and reasoning. ACM Transactions on Computational Logic 7(3), 499–562 (2006)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Lierler, Y.: Abstract answer set solvers. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 377–391. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  23. 23.
    Lierler, Y.: Abstract answer set solvers with backjumping and learning. TPLP 11(2-3), 135–169 (2011)MathSciNetzbMATHGoogle Scholar
  24. 24.
    Lifschitz, V., Razborov, A.: Why are there so many loop formulas? ACM Transactions on Computational Logic 7(2), 261–268 (2006)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Lin, F., Zhao, Y.: ASSAT: Computing answer sets of a logic program by SAT solvers. Artificial Intelligence 157(1–2), 115–137 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Lin, Z., Zhang, Y., Hernandez, H.: Fast SAT-based answer set solver. In: Proc. AAAI, pp. 92–97. AAAI Press (2006)Google Scholar
  27. 27.
    Marques-Silva, J.P., Lynce, I., Malik, S.: Conflict-driven clause learning SAT solvers. In: Biere et al [3], pp. 131–153Google Scholar
  28. 28.
    Niemelä, I.: Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25(3-4), 241–273 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Samer, M., Szeider, S.: Backdoor sets of quantified boolean formulas. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 230–243. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  30. 30.
    Simons, P., Niemelä, I., Soininen, T.: Extending and implementing the stable model semantics. Artificial Intelligence 138(1–2), 181–234 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Ward, J., Schlipf, J.: Answer set programming with clause learning. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 302–313. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  32. 32.
    Williams, R., Gomes, C.P., Selman, B.: Backdoors to typical case complexity. In: Proc. IJCAI, pp. 1173–1178. Morgan Kaufmann (2003)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Emilia Oikarinen
    • 1
  • Matti Järvisalo
    • 2
  1. 1.HIIT and Department of Information and Computer ScienceAalto UniversityFinland
  2. 2.HIIT and Department of Computer ScienceUniversity of HelsinkiFinland

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