多对数独立性愚AC^0电路

2009 24th Annual IEEE Conference on Computational Complexity Pub Date : 2009-07-15 DOI:10.1145/1754399.1754401

M. Braverman

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引用次数: 105

摘要

我们证明了多尺度AC^0电路不能区分多对数无关分布和均匀分布。这就解决了Linial和Nisan [LN90]在1990年提出的猜想。在此问题上唯一的先验进展是Bazzi [Baz07]，他证明了O(log^2 n)独立分布可以欺骗多元大小的DNF公式。Razborov [Raz08]后来对Bazzi定理给出了一个更简单的证明。

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Poly-logarithmic Independence Fools AC^0 Circuits

We prove that poly-sized AC^0 circuits cannot distinguish a poly-logarithmically independent distribution from the uniform one. This settles the 1990 conjecture by Linial and Nisan [LN90]. The only prior progress on the problem was by Bazzi [Baz07], who showed that O(log^2 n)-independent distributions fool poly-size DNF formulas. Razborov [Raz08] has later given a much simpler proof for Bazzi’s theorem.

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2009 24th Annual IEEE Conference on Computational Complexity

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