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How to Determine the Expressive Power of Constraints

Authors:

Marc GyssensAuthors Info & Claims

Constraints, Volume 4, Issue 2

Pages 113 - 131

https://doi.org/10.1023/A:1009890709297

Published: 01 May 1999 Publication History

Abstract

Some constraint languages are more powerful than others because they allow us to express a larger collection of problems. In this paper, we give a precise meaning to this concept of expressive power for constraints over finite sets of values. The central result of the paper is that the expressive power of a given set of constraint types is determined by certain algebraic properties of the underlying relations. These algebraic properties can be calculated by solving a particular constraint satisfaction problem, which we call an ’indicator problem‘. We discuss the connection between expressive power and computational complexity, and show that indicator problems provide a simple method to test for tractability.

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Cited By

Livieratos JKolaitis PKirousis L(2022)On the Computational Complexity of Non-Dictatorial AggregationJournal of Artificial Intelligence Research10.1613/jair.1.1247672(137-183)Online publication date: 4-Jan-2022
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Jonsson PLagerkvist VRoy B(2021)Fine-Grained Time Complexity of Constraint Satisfaction ProblemsACM Transactions on Computation Theory10.1145/343438713:1(1-32)Online publication date: 21-Jan-2021
https://dl.acm.org/doi/10.1145/3434387
Arenas MDiaz G(2016)The Exact Complexity of the First-Order Logic Definability ProblemACM Transactions on Database Systems10.1145/288609541:2(1-14)Online publication date: 11-May-2016
https://dl.acm.org/doi/10.1145/2886095
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Published In

cover image Constraints

Constraints Volume 4, Issue 2

May 1999

91 pages

ISSN:1383-7133

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Copyright © Copyright © 1999 Kluwer Academic Publishers.

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Kluwer Academic Publishers

United States

Publication History

Published: 01 May 1999

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Cited By

Livieratos JKolaitis PKirousis L(2022)On the Computational Complexity of Non-Dictatorial AggregationJournal of Artificial Intelligence Research10.1613/jair.1.1247672(137-183)Online publication date: 4-Jan-2022
https://dl.acm.org/doi/10.1613/jair.1.12476
Jonsson PLagerkvist VRoy B(2021)Fine-Grained Time Complexity of Constraint Satisfaction ProblemsACM Transactions on Computation Theory10.1145/343438713:1(1-32)Online publication date: 21-Jan-2021
https://dl.acm.org/doi/10.1145/3434387
Arenas MDiaz G(2016)The Exact Complexity of the First-Order Logic Definability ProblemACM Transactions on Database Systems10.1145/288609541:2(1-14)Online publication date: 11-May-2016
https://dl.acm.org/doi/10.1145/2886095
Antonopoulos TNeven FServais F(2013)Definability problems for graph query languagesProceedings of the 16th International Conference on Database Theory10.1145/2448496.2448514(141-152)Online publication date: 18-Mar-2013
https://dl.acm.org/doi/10.1145/2448496.2448514
Uppman H(2013)The complexity of three-element min-sol and conservative min-cost-homProceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I10.1007/978-3-642-39206-1_68(804-815)Online publication date: 8-Jul-2013
https://dl.acm.org/doi/10.1007/978-3-642-39206-1_68
Barto LKozik MWillard R(2012)Near Unanimity Constraints Have Bounded Pathwidth DualityProceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science10.1109/LICS.2012.24(125-134)Online publication date: 25-Jun-2012
https://dl.acm.org/doi/10.1109/LICS.2012.24
Jonsson PKuivinen FThapper J(2011)Min CSP on four elementsProceedings of the 17th international conference on Principles and practice of constraint programming10.5555/2041160.2041197(438-453)Online publication date: 12-Sep-2011
https://dl.acm.org/doi/10.5555/2041160.2041197
Bulatov AMarx D(2011)Constraint satisfaction parameterized by solution sizeProceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I10.5555/2027127.2027173(424-436)Online publication date: 4-Jul-2011
https://dl.acm.org/doi/10.5555/2027127.2027173
Willard R(2010)Testing expressibility is hardProceedings of the 16th international conference on Principles and practice of constraint programming10.5555/1886008.1886014(9-23)Online publication date: 6-Sep-2010
https://dl.acm.org/doi/10.5555/1886008.1886014
Cohen DJeavons Pivný S(2008)The expressive power of valued constraintsTheoretical Computer Science10.1016/j.tcs.2008.08.036409:1(137-153)Online publication date: 1-Dec-2008
https://dl.acm.org/doi/10.1016/j.tcs.2008.08.036
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