Constraint satisfaction dual problem

Given a constraint satisfaction problem (X,D,C), one can build a binary problem as follows:

1. for each constraint of the original problem there is a variable;
2. the domain of this variable is composed by one element for each tuple of the corresponding constraint
3. if two constraints of the original problem share some variables, a binary constraint between the corresponding variables in the new problem is given. This constraint states that the values of the new variables must be such that the corresponding values of the original variables are equal.