异或函数的协议结构

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2016-10-01 DOI:10.1109/FOCS.2016.38

Hamed Hatami, Kaave Hosseini, Shachar Lovett

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引用次数: 56

摘要

设f是一个有n个变量的布尔函数。其相关的异或函数是两方函数F(x, y) = F(x XOR y)。我们表明，在多项式因子范围内，F的确定性通信复杂性等于F的奇偶性决策树复杂性。这依赖于一种新的协议熵降技术，结合傅立叶分析和加性组合学中的现有技术。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Structure of Protocols for XOR Functions

Let f be a boolean function on n variables. Its associated XOR function is the two-party function F(x, y) = f(x xor y). We show that, up to polynomial factors, the deterministic communication complexity of F is equal to the parity decision tree complexity of f. This relies on a novel technique of entropy reduction for protocols, combined with existing techniques in Fourier analysis and additive combinatorics.

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2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)

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