The computational complexity of game trees by eigen-distribution

Authors:
ChenGuang Liu;Kazuyuki Tanaka
Affiliations:
Mathematical Institute, Tohoku University, Sendai, Japan;Mathematical Institute, Tohoku University, Sendai, Japan
Venue:
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Year:
2007

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Abstract

The AND-OR tree is an extremely simple model to compute the read-once Boolean functions. For an AND-OR tree, the eigendistribution 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.