The computational complexity of game trees by eigen-distribution

Abstract

The AND-OR tree is an extremely simple model to compute the read-once Boolean functions. For an AND-OR tree, the eigen-distribution is a special distribution on random assignments to the leaves, such that the distributional complexity of the AND-OR tree is achieved. Yao's Principle[8] showed that the randomized complexity of any function is equal to the distributional complexity of the same function. In the present work, we propose an eigen-distribution- based technique to compute the distributional complexity of read-once Boolean functions. Then, combining this technique and Yao's Principle, we provide a unifying proof way for some well-known results of the randomized complexity of Boolean functions. © Springer-Verlag Berlin Heidelberg 2007.