Complexity of query answering in logic databases with complex values

  • Evgeny Dantsin
  • Andrei Voronkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1234)


This paper studies the complexity of the query answering problem in logic databases with complex values. Logic databases are represented as Horn clause logic programs; complex values are described in a data model based on equational theories. As examples of complex values, we consider trees, bags and finite sets. We give a natural sufficient condition under which the query answering problem for non-recursive programs with complex values is in NEXP. In particular, logic programs with trees, bags and finite sets satisfy this condition. We also show that the query answering problem for non-recursive range restricted logic programs is NEXP-hard. Thereby, the query answering problem for logic databases with trees, bags and sets turns out to be NEXP-complete.


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  1. 1.
    S. Abiteboul and S. Grumbach. A rule-based language with functions and sets. ACM Transactions on Database Systems, 16(1):1–30, 1991.Google Scholar
  2. 2.
    S. Abiteboul and C. Beeri. The power of languages for the manipulation of complex values. VLDB Journal, 4:727–794, 1995.Google Scholar
  3. 3.
    K.R. Apt. Logic programming. In J. Van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B: Formal Methods and Semantics, chapter 10, pages 493–574. Elsevier Science, Amsterdam, 1990.Google Scholar
  4. 4.
    C. Beeri, S. Naqvi, O. Schmueli, and S. Tsur. Set constructors in a logic database language. Journal of Logic Programming, 10:181–232, 1991.Google Scholar
  5. 5.
    B. Börger, E. Grädel, and Y. Gurevich. The Classical Decision Problem. Springer Verlag, 1997.Google Scholar
  6. 6.
    E. Dantsin, T. Eiter, G. Gottlob, and A. Voronkov. Complexity and expressive power of logic programming. In CCC'97, 1997. To appear.Google Scholar
  7. 7.
    E. Dantsin and A. Voronkov. Complexity of query answering in logic databases with complex values. UPMAIL technical report, Uppsala University, Computing Science Department, 1997. Scholar
  8. 8.
    A. Dovier, E.G. Omodeo, E. Pontelli, and G. Rossi. {log}: A language for programming in logic with finite sets. Journal of Logic Programming, 28(1):1–44, 1996.Google Scholar
  9. 9.
    M. Gabbrielli, G.M. Dore, and G. Levi. Observable semantics for constraint logic programs. Journal of Logic and Computation, 5(2):133–171, 1995.Google Scholar
  10. 10.
    J.H. Gallier and S. Raatz. Extending SLD-resolution to equational Horn clauses using E-unification. Journal of Logic Programming, 6(3):3–44, 1989.Google Scholar
  11. 11.
    J. Jaffar and M. Maher. Constraint logic programming: a survey. Journal of Logic Programming, 19,20:503–581, 1994.Google Scholar
  12. 12.
    B. Jayaraman and D.A. Plaisted. Programming with equations, subsets and relations. In Proc. NACLP'89, Cleveland, 1989. MIT Press.Google Scholar
  13. 13.
    D. Kapur and P. Narendran. NP-completeness of the set unification and matching problems. In J. Siekmann, editor, Proc. 8th CADE, volume 230 of Lecture Notes in Computer Science, 1986.Google Scholar
  14. 14.
    G.M. Kuper. Logic programming with sets. Journal of Computer and System Sciences, 41:44–64, 1990.Google Scholar
  15. 15.
    G.M. Kuper and M.Y. Vardi. The logical data model. ACM Transactions on Database Systems, 18(3):379–413, 1993.Google Scholar
  16. 16.
    J.W. Lloyd. Foundations of Logic Programming (2nd edition). Springer Verlag, 1987.Google Scholar
  17. 17.
    M.J. Maher. A CLP view of logic programming. In Proc. Conf. on Algebraic and Logic Programming, volume 632 of Lecture Notes in Computer Science, pages 364–383, October 1992.Google Scholar
  18. 18.
    T. Munakata. Notes on implementing sets in Prolog. Communications of the ACM, 35(3):112–120, 1992.Google Scholar
  19. 19.
    C.H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.Google Scholar
  20. 20.
    O. Shmueli, S. Tsur, and C. Zaniolo. Compilation of set terms in the logic data language (LDL). Journal of Logic Programming, 12(1):89–119, 1992.Google Scholar
  21. 21.
    G. Smolka and R. Treinen. Records for logic programming. Journal of Logic Programming, 18:229–258, 1994.Google Scholar
  22. 22.
    M. Vardi. The complexity of relational query languages. In Proc. 14th ACM STOC, 1982.Google Scholar
  23. 23.
    A. Voronkov. Logic programming with bounded quantifiers revisited. UPMAIL Technical Report, Uppsala University, Computing Science Department, 1997, to appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Evgeny Dantsin
    • 1
  • Andrei Voronkov
    • 2
  1. 1.Steklov Institute of Mathematics at St.PetersburgSt.PetersburgRussia
  2. 2.Computing Science DepartmentUppsala UniversityUppsalaSweden

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