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.
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Liu, C., Tanaka, K. (2007). The Computational Complexity of Game Trees by Eigen-Distribution. In: Dress, A., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2007. Lecture Notes in Computer Science, vol 4616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73556-4_34
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DOI: https://doi.org/10.1007/978-3-540-73556-4_34
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