An Algebraic Approach to the Complexity of Generalized Conjunctive Queries

  • Michael Bauland
  • Philippe Chapdelaine
  • Nadia Creignou
  • Miki Hermann
  • Heribert Vollmer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3542)


Conjunctive-query containment is considered as a fundamental problem in database query evaluation and optimization. Kolaitis and Vardi pointed out that constraint satisfaction and conjunctive query containment are essentially the same problem. We study the Boolean conjunctive queries under a more detailed scope, where we investigate their counting problem by means of the algebraic approach through Galois theory, taking advantage of Post’s lattice. We prove a trichotomy theorem for the generalized conjunctive query counting problem, showing this way that, contrary to the corresponding decision problems, constraint satisfaction and conjunctive-query containment differ for other computational goals. We also study the audit problem for conjunctive queries asking whether there exists a frozen variable in a given query. This problem is important in databases supporting statistical queries. We derive a dichotomy theorem for this audit problem that sheds more light on audit applicability within database systems.


Boolean Function Constraint Satisfaction Problem Algebraic Approach Conjunctive Normal Form Satisfying Assignment 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Michael Bauland
    • 1
  • Philippe Chapdelaine
    • 2
  • Nadia Creignou
    • 3
  • Miki Hermann
    • 4
  • Heribert Vollmer
    • 1
  1. 1.Theoretische InformatikUniversität HannoverGermany
  2. 2.GREYC (UMR 6072)Université de CaenFrance
  3. 3.LIF (UMR 6166)Univ. de la MéditerranéeFrance
  4. 4.LIX (UMR 7161)École PolytechniqueFrance

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