Redundant hidden variables in finite domain constraint problems

Abstract

We study finite domain constraint problems with hidden variables and the possible redundancy of some of the hidden variables. These are problems where a subset of the variables are chosen to be “visible”, and the others are therefore “hidden”. Visible variables are the variables of interest from the outside, in the sense that a solution involves only them. For variable redundancy we mean that the elimination of a variable, together with all the constraints connecting it, does not change the set of solutions of the given problem. We propose several sufficient conditions for hidden variable redundancy and we develop algorithms, based on such conditions, which remove the variables found to be redundant. This, combined with other preprocessing techniques which remove other kinds of redundancy (tuple redundancy, such as the local consistency algorithms, or also constraint redundancy), can be very helpful for constraint solving. In fact, the number of variables coincide with the depth of the search tree. Therefore removing variables means shortening the search tree itself.