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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Jeavons, P., Cohen, D. & Gyssens, M. How to Determine the Expressive Power of Constraints. Constraints 4, 113–131 (1999). https://doi.org/10.1023/A:1009890709297
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DOI: https://doi.org/10.1023/A:1009890709297