In this paper a theory of game tree algorithms is presented, entirely based upon the concept of a solution tree. Two types of solution trees are distinguished: max and min trees. Every game tree algorithm tries to prune as many nodes as possible from the game tree. A cut-off criterion in terms of solution trees will be formulated, which can be used to eliminate nodes from the search without affecting the result. Further, we show that any algorithm actually constructs a superposition of a max and a min solution tree. Finally, we will see how solution trees and the related cutoff criterion are applied in major game tree algorithms like alphabeta and MTD.

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Theoretical Computer Science
Erasmus School of Economics

Pijls, W., & de Bruin, A. (2001). Game tree algorithms and solution trees. Theoretical Computer Science, 252(1-2), 197–215. doi:10.1016/S0304-3975(00)00082-7