Alpha-Beta Pruning Under Partial Orders
نویسندگان
چکیده
Alpha-beta pruning is the algorithm of choice for searching game trees with position values taken from a totally ordered set, such as the set of real numbers. We generalize to game trees with position values taken from a partially ordered set, and prove necessary and sufficient conditions for alpha-beta pruning to be valid. Specifically, we show that shallow pruning is possible if and only if the value set is a lattice, and full alphabeta pruning is possible if and only if the value set is a distributive lattice. We show that the resulting technique leads to substantial improvements in the speed of algorithms dealing with card play in contract bridge.
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