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Linear constraint query languages expressive power and complexity

  • Stéphane Grumbach
  • Jianwen Su
  • Christophe Tollu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 960)

Abstract

We give an AC0 upper bound on the complexity of first-oder queries over (infinite) databases defined by restricted linear constraints. This result enables us to deduce the non-expressibility of various usual queries, such as the parity of the cardinality of a set or the connectivity of a graph in first-order logic with linear constraints.

Keywords

Boolean Function Linear Constraint Atomic Formula Relational Algebra Disjunctive Normal Form 
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. [AHV94]
    S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1994.Google Scholar
  2. [Ban78]
    F. Bancilhon. On the completeness of query languages for relational data bases. In Proc. 7th Symp. on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, pages 112–123. Springer-Verlag, 1978.Google Scholar
  3. [Bea76]
    D. R. Bean. Recursive Euler and Hamilton paths. In Proc. American Mathematical Society, volume 55, pages 385–394, 1976.Google Scholar
  4. [BKR86]
    M. Ben-Or, D. Kozen, and J. Reif. The complexity of elementary algebra and geometry. Journal of Computer and System Sciences, 32(2):251–264, April 1986.CrossRefGoogle Scholar
  5. [CH80]
    A. K. Chandra and D. Harel. Computable queries for relational data bases. Journal of Computer and System Sciences, 21(2):156–78, 1980.CrossRefGoogle Scholar
  6. [Cod70]
    E.F. Codd. A relational model of data for large shared data banks. Communications of ACM, 13:6:377–387, 1970.CrossRefGoogle Scholar
  7. [Col75]
    G. E. Collins. Quantifier elimination for real closed fields by cylindric decompositions. In Proc. 2nd GI Conf. Automata Theory and Formal Languages, volume 35 of Lecture Notes in Computer Science, pages 134–83. Springer-Verlag, 1975.Google Scholar
  8. [FSS84]
    M. Furst, J. B. Saxe, and M. Sipser. Parity, circuits, and the polynomialtime hierarchy. Math. Syst. Theory, 17:13–27, 1984.Google Scholar
  9. [GS94]
    S. Grumbach and J. Su. Finitely representable databases (extended abstract). In Proc. 13th ACM Symp. on Principles of Database Systems, 1994.Google Scholar
  10. [GS95]
    S. Grumbach and J. Su. Finitely representable databases, 1995. Full version of [GS94], invited to JCSS (Special Issue of PODS '94).Google Scholar
  11. [Har91]
    D. Harel. Hamiltonian paths in infinite graphs. Israel Journal of Mathematics, 76:317–336, 1991.Google Scholar
  12. [HH93]
    T. Hirst and D. Harel. Completeness results for recursive data bases. In Proc. 12th ACM Symp. on Principles of Database Systems, pages 244–252, 1993.Google Scholar
  13. [HH94]
    T. Hirst and D. Harel. Recursive model theory, 1994. Draft.Google Scholar
  14. [Joh90]
    D. Johnson. A catalog of complexity classes. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A, Elsevier-North Holland, 1990.Google Scholar
  15. [KG94]
    P. C. Kanellakis and D. Q. Goldin. Constraint programming and database query languages. In Proc. 2nd Conference on Theoretical Aspects of Computer Software (TACS), April 1994. (To appear in a LNCS volume, Springer-Verlag).Google Scholar
  16. [KG95]
    P. C. Kanellakis and D. Q. Goldin. Personal communication, 1995.Google Scholar
  17. [KKR90]
    P. Kanellakis, G. Kuper, and P. Revesz. Constraint query languages. In Proc. 9th ACM Symp. on Principles of Database Systems, pages 299–313, Nashville, 1990.Google Scholar
  18. [Mos57]
    A. Mostowski. On recursive models of formalized arithmetics. Bulletin de l'Académie Polonaise des Sciences, III, 5:705–710, 1957.Google Scholar
  19. [Par78]
    J. Paredaens. On the expressive power of the relational algebra. Information Processing Letters, 7(2):107–111, February 1978.Google Scholar
  20. [PVV94]
    J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In Proc. 13th ACM Symp. on Principles of Database Systems, pages 279–88, 1994.Google Scholar
  21. [PVV95]
    J. Paredaens, J. Van den Bussche, and D. Van Gucht. First-order Queries on Finite Structures over the Reals. In Proc. 10th IEEE Symp. on Logic in Computer Science, to appear.Google Scholar
  22. [Sch86]
    A. Schrijver. Theory of Linear and Integer Programming. Wiley, Chichester, 1986.Google Scholar
  23. [Va94]
    J. Väänänen. Personal communication.Google Scholar
  24. [Vau60]
    R. L. Vaught. Sentences true in all constructive models. Journal of Symbolic Logic, 25(1):39–53, March 1960.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Stéphane Grumbach
    • 1
  • Jianwen Su
    • 2
  • Christophe Tollu
    • 3
  1. 1.INRIA at Santa BarbaraLe ChesnayFrance
  2. 2.Dept. of Computer Science INRIAUniversity of CaliforniaSanta BarbaraUSA
  3. 3.LIPN-URA 1507, Institut GaliléeUniversité Paris-NordVilletaneuseFrance

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