@ -622,7 +622,7 @@ Applies the AC-3 arc-consistency algorithm. Similar to forward checking, but che
Specifically: following a new variable assignment, AC-3 examines all constraints that link exactly two unassigned variables. It checks that each variable has at least one value in its domain that can be paired with the other to satisfy the constraint (this pair comprises the eponymous @italic{arc}). If no such pair exists, then the constraint can never be satisfied, so the new variable assignment must fail.
``So AC-3 is a superset of @racket[forward-check]?" Yes. Both techniques examine two-arity constraints after variable @racket[_name] has been assigned a value. Forward checking, however, only examines two-arity functions that include variable @racket[_name] in the constraint. Whereas AC-3 checks @italic{all} two-arity functions (even those that don't include @racket[_name]).
``So AC-3 is a superset of @racket[forward-check]?'' Yes. Both techniques examine two-arity constraints after variable @racket[_name] has been assigned a value. Forward checking, however, only examines two-arity functions that include variable @racket[_name] in the constraint. Whereas AC-3 checks @italic{all} two-arity functions (even those that don't include @racket[_name]).
In this way, AC-3 can detect inconsistencies that forward checking would miss. For instance, consider a CSP with three variables @italic{a} @italic{b} and @italic{c}, and three constraints @italic{ab}, @italic{ac}, and @italic{ab}. We assign a value to @italic{a}. Forward checking would then check constraints @italic{ab} and @italic{ac}, perhaps removing values from the domains of @italic{b} and @italic{c} to be consistent with the new value of @italic{a}. These domain reductions, however, might be inconsistent with constraint @italic{bc}. Forward checking won't notice this, because it never tests @italic{bc}. But AC-3 does test @italic{bc}, so it would notice the inconsistency.
