Constructing Constraints

It is well-known that there is a trade-off between the expressive power of a constraint language and the tractability of the problems it can express. But how can you determine the expressive power of a given constraint language, and how can you tell if problems expressed in that language are tractable? In this paper we discuss some general approaches to these questions. We show that for languages over a finite domain the concept of an 'indicator problem' gives a universal construction for any constraint within the expressive power of a language. We also discuss the fact that all known tractable languages over finite domains are characterised by the presence of a particular solution to a corresponding indicator problem, and raise the question of whether this is a universal property of tractable languages.

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