How to Determine the Expressive Power of Constraints

Authors:
Peter Jeavons;David Cohen;Marc Gyssens
Affiliations:
Department of Computer Science, Royal Holloway, University of London, UK;Department of Computer Science, Royal Holloway, University of London, UK;Department WNI, University of Limburg, B-3590 Diepenbeek, Belgium
Venue:
Constraints
Year:
1999

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Abstract

Some constraint languages are more powerfulthan others because they allow us to express a larger collectionof problems. In this paper, we give a precise meaning to thisconcept of expressive power for constraints over finite setsof values. The central result of the paper is that the expressivepower of a given set of constraint types is determined by certainalgebraic properties of the underlying relations. These algebraicproperties can be calculated by solving a particular constraintsatisfaction problem, which we call an ’indicator problem‘. Wediscuss the connection between expressive power and computationalcomplexity, and show that indicator problems provide a simplemethod to test for tractability.