Assumptions
In this article, a constraint satisfaction problem is defined as a set of variables, a set of domains, and a set of constraints. Variables and domains are associated: the domain of a variable contains all values the variable can take. A constraint is composed of a sequence of variables, called its scope, and a set of their evaluations, which are the evaluations satisfying the constraint.
The constraint satisfaction problems referred to in this article are assumed to be in a special form. A problem is in normalized form, respectively regular form, if every sequence of variables is the scope of at most one constraint or exactly one constraint, respectively. The assumption of regularity done only for binary constraints leads to the standardized form. These conditions can always be enforced by combining all constraints over a sequence of variables into a single one and/or adding a constraint that is satisfied by all values of a sequence of variables.
In the figures used in this article, the lack of links between two variables indicate that either no constraint or a constraint satisfied by all values exists between these two variables.
Read more about this topic: Local Consistency
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