The first stage in constraint satisfaction is constraint propagation, where any dependencies between constraints are exploited to introduce more constraint and thus reduce the solution space. Then follows a search where variables are assigned values and matched against current constraints; this involves further constraint propagation and backtracking from failures. A solution is produced when a single set of values fits the final reduced set of constraints. An overconstrained problem will have no solution and an under-constrained problem may produce many alternative solutions.
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