Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds on the Size of Small Depth Circuits for Approximating Majority   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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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex