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The basic idea of constraint propagation is to activate the propagators of constraints whenever the domains of the variables in the constraints are updated.
The actions of constraint propagators are to reduce the domains of variables.
It can be used to program not only constraint propagators but also constraint reasoning rules.
The filters and constraint propagators serve to prune off branches of the tree that cannot lead to solutions.
A propagator for a constraint that performs forward checking is activated whenever the constraint becomes unary.
While many useful constraints have polynomial-time arc-consistency propagators, some exist for which this task is intractable.
The propagators for each variable are independent; thus, the generalization obtained when using the solver is the one obtained with veto vote.
As examples, we present a weak arc-consistency propagator for the all distinct constraint and a hybrid algorithm for n-ary linear equality constraints.
