Article

Definability and Descriptive Complexity on Databases of Bounded Tree-Width

Authors:

Julian MariñoAuthors Info & Claims

ICDT '99: Proceedings of the 7th International Conference on Database Theory

Pages 70 - 82

Published: 10 January 1999 Publication History

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 C^k+3, the (k + 3)-variable fragment of first-order logic with counting.

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Atserias AKolaitis PWu WGorla D(2021)On the expressive power of homomorphism countsProceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science10.1109/LICS52264.2021.9470543(1-13)Online publication date: 29-Jun-2021
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Grohe MNeuen DBouyer P(2019)Canonisation and definability for graphs of bounded rank widthProceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3470152.3470180(1-13)Online publication date: 24-Jun-2019
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Grußien BAceto LIngólfsdóttir A(2017)Capturing polynomial time using modular decompositionProceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3329995.3330058(1-12)Online publication date: 20-Jun-2017
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Index Terms

Definability and Descriptive Complexity on Databases of Bounded Tree-Width
1. Information systems
  1. Data management systems
    1. Query languages
2. Theory of computation
  1. Formal languages and automata theory
  2. Logic
    1. Constraint and logic programming

Index terms have been assigned to the content through auto-classification.

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cover image Guide Proceedings

ICDT '99: Proceedings of the 7th International Conference on Database Theory

January 1999

487 pages

ISBN:3540654526

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 10 January 1999

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Cited By

Atserias AKolaitis PWu WGorla D(2021)On the expressive power of homomorphism countsProceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science10.1109/LICS52264.2021.9470543(1-13)Online publication date: 29-Jun-2021
https://dl.acm.org/doi/10.1109/LICS52264.2021.9470543
Grohe MNeuen DBouyer P(2019)Canonisation and definability for graphs of bounded rank widthProceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3470152.3470180(1-13)Online publication date: 24-Jun-2019
https://dl.acm.org/doi/10.5555/3470152.3470180
Grußien BAceto LIngólfsdóttir A(2017)Capturing polynomial time using modular decompositionProceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3329995.3330058(1-12)Online publication date: 20-Jun-2017
https://dl.acm.org/doi/10.5555/3329995.3330058
Kiefer SPonomarenko ISchweitzer PAceto LIngólfsdóttir A(2017)The weisfeiler-leman dimension of planar graphs is at most 3Proceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3329995.3330042(1-12)Online publication date: 20-Jun-2017
https://dl.acm.org/doi/10.5555/3329995.3330042
Dawar A(2015)The nature and power of fixed-point logic with countingACM SIGLOG News10.1145/2728816.27288202:1(8-21)Online publication date: 28-Jan-2015
https://dl.acm.org/doi/10.1145/2728816.2728820
Grohe M(2012)Fixed-point definability and polynomial time on graphs with excluded minorsJournal of the ACM10.1145/2371656.237166259:5(1-64)Online publication date: 5-Nov-2012
https://dl.acm.org/doi/10.1145/2371656.2371662
Grohe M(2011)From polynomial time queries to graph structure theoryCommunications of the ACM10.1145/1953122.195315054:6(104-112)Online publication date: 1-Jun-2011
https://dl.acm.org/doi/10.1145/1953122.1953150
Grohe M(2010)Fixed-point definability and polynomial time on chordal graphs and line graphsFields of logic and computation10.5555/1983702.1983721(328-353)Online publication date: 1-Jan-2010
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Schweikardt NSchwentick TSegoufin L(2010)Database theoryAlgorithms and theory of computation handbook10.5555/1882723.1882742(19-19)Online publication date: 1-Jan-2010
https://dl.acm.org/doi/10.5555/1882723.1882742
Grohe M(2009)Fixed-point definability and polynomial timeProceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic10.5555/1807662.1807667(20-23)Online publication date: 7-Sep-2009
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