Bounds on the Size of Small Depth Circuits for Approximating Majority

Details Bounds on the Size of Small Depth Circuits for Approximating Majority Bounds on the Size of Small Depth Circuits for Approximating Majority

2009-01-31

arxiv.org/abs/0902.0047v1

Computer Science

Computational Complexity

12 pages

Scientific paper

In this paper, we show that for every constant $0 < \epsilon < 1/2$ and for every constant $d \geq 2$, the minimum size of a depth $d$ Boolean circuit that $\epsilon$-approximates Majority function on $n$ variables is exp$(\Theta(n^{1/(2d-2)}))$. 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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