A Theory of Game Trees, Based on Solution Trees

In this paper, a theory of game tree algorithms is presented, entirely based upon the concept of solution tree. Two types of solution trees are distinguished: max and min solution trees respectively. We show that a game tree algorithm actually constructs a superposition of a max and a min solution tree. For algorithms searching a game tree, a cutoo criterion is suitable. A cut-oo criterion in terms of solution trees will be formulated, which can be used to eliminate nodes from the search without aaecting the result. Finally, we will see, how solution trees and the related cutoo criterion are applied in the major game tree algorithms.