# Houria III

Constraints allow programmers and users to state declaratively a relation that should be maintained, rather than requiring them to write procedures to maintain the relation themselves. They are thus useful in many applications such as user interface and simulation packages. In many situations, it is desirable to be able to state both hard and soft constraints. The hard constraints must hold, and the soft constraints are satisfied as much as possible, depending on the criterion used. A constraint hierarchy consists of a set of constraints, each labeled as either hard or soft at some strength, and each soft constraint is weighted by a real weight. The existing solvers for satisfying constraint hierarchy impose that every class of soft constraints labeled by a strength contains constraints with the same weight. This paper surmounts this restriction by presenting an incremental solver that proposes extended definitions of constraint hierarchy. This solver handles different classes of soft constraints labeled with strengths where each class may contain weighted constraints. The criterion of comparison used in this solver is global. It allows the comparison of some valuations, which are not comparable by local criteria used in some existing solvers. This criterion is the generalization of the global criterion used in other solvers.

## References in zbMATH (referenced in 1 article , 1 standard article )

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