Bounds on the Size of Small Depth Circuits for Approximating Majority

Kazuyuki Amano

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arXiv · 0902.0047

Bounds on the Size of Small Depth Circuits for Approximating Majority

Kazuyuki Amano

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Abstract

In this paper, we show that for every constant $0 < ε< 1/2$ and for every constant $d \geq 2$, the minimum size of a depth $d$ Boolean circuit that $ε$-approximates Majority function on $n$ variables is exp$(Θ(n^{1/(2d-2)}))$. The lower bound for every $d \geq 2$ and the upper bound for $d=2$ have been previously shown by O'Donnell and Wimmer [ICALP'07], and the contribution of this paper is to give a matching upper bound for $d \geq 3$.

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BibTeX RIS

Kazuyuki Amano. 2009-01-31. Bounds on the Size of Small Depth Circuits for Approximating Majority. https://arxiv.org/abs/0902.0047

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