Definability and Descriptive Complexity on Databases of Bounded Tree-Width

  • Martin Grohe
  • Julian Mariño
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1540)

Abstract

We study the expressive power of various query languages on relational databases of bounded tree-width.

Our first theorem says that fixed-point logic with counting captures polynomial time on classes of databases of bounded tree-width. This result should be seen on the background of an important open question of Chandra and Harel [7] asking whether there is a query language capturing polynomial time on unordered databases. Our theorem is a further step in a larger project of extending the scope of databases on which polynomial time can be captured by reasonable query languages.

We then prove a general definability theorem stating that each query on a class of databases of bounded tree-width which is definable in monadic second-order logic is also definable in fixed-point logic (or datalog). Furthermore, for each k ≥ 1 the class of databases of tree-width at most k is definable in fixed-point logic. These results have some remarkable consequences concerning the definability of certain classes of graphs.

Finally, we show that each database of tree-width at most k can be characterized up to isomorphism in the language Ck+3, the (k + 3)-variable fragment of firstorder logic with counting.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Martin Grohe
    • 1
  • Julian Mariño
    • 1
  1. 1.Institut für mathematische LogikFreiburgGermany

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