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Computing Stable Models: Worst-Case Performance Estimates

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Logic Programming (ICLP 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2401))

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Abstract

We study algorithms for computing stable models of propositional logic programs and derive estimates on their worst-case performance that are asymptotically better than the trivial bound of O(m2n), where m is the size of an input program and n is the number of its atoms. For instance, for programs, whose clauses consist of at most two literals (counting the head) we design an algorithm to compute stable models that works in time O(m × 1.44225n). We present similar results for several broader classes of programs, as well.

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References

  1. K. Apt. Logic programming. In J. van Leeuven, editor, Handbook of theoretical computer science, pages 493–574. Elsevier, Amsterdam, 1990.

    Google Scholar 

  2. P. A. Bonatti and T. Eiter. Querying Disjunctive Databases Through Nonmonotonic Logics. Theoretical Computer Science, 160:321–363, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  3. P. Cholewiński and M. Truszczyński. Extremal problems in logic programming and stable model computation. Journal of Logic Programming, 38:219–242, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Dix. A classification theory of semantics of normal logic programs: Ii. weak properties. Fundamenta Informaticae, 22(3):257–288, 1995.

    MATH  MathSciNet  Google Scholar 

  5. T. Eiter, W. Faber, N. Leone, and G. Pfeifer. Declarative problem-solving in DLV. In Jack Minker, editor, Logic-Based Artificial Intelligence, pages 79–103. Kluwer Academic Publishers, Dordrecht, 2000.

    Google Scholar 

  6. M. Gelfond and V. Lifschitz. The stable semantics for logic programs. In R. Kowalski and K. Bowen, editors, Proceedings of the 5th International Conference on Logic Programming, pages 1070–1080. MIT Press, 1988.

    Google Scholar 

  7. D. E. Knuth. The Art of Computer Programming, volume 3. Addison Wesley, 1998. Second edition.

    Google Scholar 

  8. O. Kullmann. New methods for 3-SAT decision and worst-case analysis. Theoretical Computer Science, pages 1–72, 1999.

    Google Scholar 

  9. J. W. Moon and L. Moser. On cliques in graphs. Israel J. Math, pages 23–28, 1965.

    Google Scholar 

  10. W. Marek, A. Nerode, and J. B. Remmel. The stable models of predicate logic programs. Journal of Logic Programming, 21(3):129–154, 1994.

    MATH  MathSciNet  Google Scholar 

  11. B. Monien and E. Speckenmeyer. Solving satisfiability in less than 2n steps. Discrete Applied Mathematics, pages 287–295, 1985.

    Google Scholar 

  12. W. Marek and M. Truszczyński. Nonmonotonic logics; context-dependent reasoning. Springer-Verlag, Berlin, 1993.

    Google Scholar 

  13. I. Niemelä and P. Simons. Extending the smodels system with cardinality and weight constraints. In J. Minker, editor, Logic-Based Artificial Intelligence, pages 491–521. Kluwer Academic Publishers, 2000.

    Google Scholar 

  14. V. S. Subrahmanian, D. Nau, and C. Vago. WFS + branch bound = stable models. IEEE Transactions on Knowledge and Data Engineering, 7:362–377, 1995.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-661, Warsaw, Poland

    Zbigniew Lonc

  2. Department of Computer Science, University of Kentucky, Lexington, KY, 40506-0046, USA

    Mirosław Truszczyński

Authors
  1. Zbigniew Lonc
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  2. Mirosław Truszczyński
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Software Engineering, University of Melbourne, 221 Bouverie St., Carlton, 3053, Australia

    Peter J. Stuckey

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© 2002 Springer-Verlag Berlin Heidelberg

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Lonc, Z., Truszczyński, M. (2002). Computing Stable Models: Worst-Case Performance Estimates. In: Stuckey, P.J. (eds) Logic Programming. ICLP 2002. Lecture Notes in Computer Science, vol 2401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45619-8_24

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  • DOI: https://doi.org/10.1007/3-540-45619-8_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43930-1

  • Online ISBN: 978-3-540-45619-3

  • eBook Packages: Springer Book Archive

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