# Generalized arc consistency

### From Glossary

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

A variable 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 is arc-consistent with another variable if for every value in the domain of there exists a value in the domain of such that the binary constraint is satisfied. A binary constraint is arc-consistent if both of its variables are arc-consistent with respect to each other.

See also: