Query Evaluation via Tree-Decompositions

Extended Abstract
  • Jörg Flum
  • Markus Frick
  • Martin Grohe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1973)

Abstract

A number of efficient methods for evaluating first-order and monadic-second order queries on finite relational structures are based on tree-decompositions of structures or queries. We systematically study these methods. In the first-part of the paper we consider tree-like structures. We generalize a theorem of Courcelle [7] by showing that on such structures a monadic second-order formula (with free first-order and second-order variables) can be evaluated in time linear in the structure size plus the size of the output. In the second part we study tree-like formulas. We generalize the notions of acyclicity and bounded tree-width from conjunctive queries to arbitrary first-order formulas in a straightforward way and analyze the complexity of evaluating formulas of these fragments. Moreover, we show that the acyclic and bounded tree-width fragments have the same expressive power as the well-known guarded fragment and the finite-variable fragments of first-order logic, respectively.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jörg Flum
    • 1
  • Markus Frick
    • 1
  • Martin Grohe
    • 2
  1. 1.Institut für Mathematische LogikAlbert-Ludwigs-Universität FreiburgFreiburgGermany
  2. 2.Department of Mathematics, Statistics, and Computer ScienceChicagoUSA

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