# 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.

# Arc consistency

A consistency property in constraint programming used as a basis for inference. A variable $LaTeX: x$ is arc-consistent with another variable $LaTeX: y$ if for every value in the domain of $LaTeX: x$ there exists a value in the domain of $LaTeX: y$ such that the binary constraint $LaTeX: C(x,y)$ is satisfied. A binary constraint $LaTeX: C(x,y)$ is arc-consistent if both of its variables are arc-consistent with respect to each other.