# Generalized arc consistency

An extension of arc consistency to constraints with more than two variables in their scope.

A variable $LaTeX: x$ is generalized arc consistent (GAC) with a constraint if every value of the variable can be extended to all the other variables of the constraint in such a way the constraint is satisfied.

Generalized arc consistency is one of the most commonly enforced forms of consistency in constraint programming.

GAC has also been called: hyper-arc consistency and domain consistency.

# Scope

The scope of a constraint is the set of directly constrained variables. For example, in the constraint $LaTeX: x \neq y$, the set $LaTeX: \{x,y\}$ is the scope.