Constraints on finite domains and intervals

Here, we discuss two types of numerical constraint which differ in that the associated solvers are less ambitious: their answers are approximate in the sense that they provide possible ranges for the variables without guaranteeing that the system of equations is actually satisfiable. However, failure guarantees that the system is unsatisfiable.

The main advantage of these solvers is their low cost. They require the use of enumerations, which are generally sophisticated, but this is offset by the fact that technological advances in this field are very significant. In practice, finite-domain constraints have been the most successful on combinatorial problems. As for interval constraints, which are more recent and, in a way, more general, they are very promising insofar as they can be used to finely solve non-linear equations.