Discussion
Why is strong n consistency not used in practice?
Answer: A
Enforcing consistency at every level up to the number of variables takes exponential time, so the theoretical prize of a backtrack free search is paid for in advance at the same price. In practice arc consistency, occasionally strengthened, is the sweet spot. Constraint arity, domain uniformity and solution knowledge are not the obstacle. A guarantee whose cost equals the cost of the thing it guarantees is a theoretical result rather than a practical technique, and recognising that is what keeps effort where it pays.
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