 Constraint propagation

Constraint propagation repeatedly removes variable values incompatible with local consequences of a constraint satisfaction problem. The goal is to reduce the remaining search while preserving all genuine solutions. For $X<Y$ with domains $\{1,2\}$, enforcing support removes two from $X$ and one from $Y$, leaving the forced pair $(1,2)$. Arc consistency checks support across binary constraints; dedicated global-constraint propagators can reason about larger sets together. Reaching a propagation fixed point does not generally prove that the whole problem has a solution, because locally supported choices can still conflict globally.