On the Kolmogorov expressive power of boolean query languages

  • Jerzy Tyszkiewicz
Contributed Papers Query Languages I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 893)

Abstract

We develop a Kolmogorov complexity based tool to measure expressive power of query languages over finite structures. It works for sentences (i.e., boolean queries), and gives a meaningful definition of the expressive power of a query language in a single finite model.

The notion of Kolmogorov expressive power of a boolean query language L in a finite model A is defined by considering two values: the Kolmogorov complexity of the isomorphism type of A, equal to the length of the shortest binary description of this type, and the number of bits of this description that can be reconstructed from truth values of all queries from L in A. The closer is the second value to the first, the more expressive is the query language. After giving the definitions and proving that they are correct, we concentrate our efforts on first order logic and its powerful extensions: inflationary fixpoint logic and partial fixpoint logic. We explore some connections between the proposed Kolmogorov expressive power of boolean queries in these languages and their standard expressive power. We show that, except of being of interest for its own, our notion may have important diagnostic value for database query optimisation.

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References

  1. [ACV]
    S. Abiteboul, K. Compton and V. Vianu, ‘Queries are easier than you thought (probably)', in: Proc. ACM Symp. on Principles of Database Systems, 1992.Google Scholar
  2. [AG]
    S. Abiteboul and A. Van Gelder, ‘Optimizing active databases using the split technique', in: Proc. ICDT'92, Springer Lecture Notes in Computer Science 646.Google Scholar
  3. [AV1]
    S. Abiteboul and V. Vianu, ‘Datalog extensions for database queries and updates', Journal of Computer and System Sciences, 43(1991), pp. 62–124.CrossRefGoogle Scholar
  4. [AV2]
    S. Abiteboul and V. Vianu, ‘Generic computation and its complexity', in: Proc. ACM SIGACT Symp. on the Theory of Computing, 1991, pp. 209–219.Google Scholar
  5. [Ch]
    A. Chandra, ‘Programming primitives for database languages', in: Proc. ACM Symp. on Principles of Programming Languages 1982, pp. 50–62.Google Scholar
  6. [CH]
    A. Chandra and D. Harel, ‘Computable queries for relational data bases', Journal of Computer and System Sciences 21(1980), pp. 156–178.CrossRefGoogle Scholar
  7. [D]
    A. Dawar, ‘Feasible computation through model theory', PhD Thesis, University of Pennsylvania, 1993.Google Scholar
  8. [GS]
    Y. Gurevich and S. Shelah, ‘Fixed-point extensions of first-order logic', Annals of Pure and Applied Logic, 32(1986), pp. 265–280.CrossRefGoogle Scholar
  9. [I]
    N. Immerman, ‘Languages that capture complexity classes', SIAM Journal of Computing 16(1987).Google Scholar
  10. [LV1]
    M. Li and P. Vitányi, ‘Kolmogorov complexity and its applications', in: J. van Leeuven (ed.) Handbook of Theoretical Computer Science, North Holland, Amsterdam, 1990.Google Scholar
  11. [LV2]
    M. Li and P. Vitányi, An introduction to Kolmogorov complexity and its applications, Springer Verlag, New York, 1993.Google Scholar
  12. [V]
    M. Vardi, ‘Complexity of relational query languages', Proc. 14th Symposium on Theory of Computation 1982, pp. 137–146.Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Jerzy Tyszkiewicz
    • 1
  1. 1.Mathematische Grundlagen der InformatikRWTH AachenAachenGermany

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