Abstract
We show that every languageL in the class ACC can be recognized by depth-two deterministic circuits with a symmetric-function gate at the root and\(2^{\log ^{O(1)} n} \) AND gates of fan-in logO(1) n at the leaves, or equivalently, there exist polynomialsp n (x 1 ,..., x n ) overZ of degree logO(1) n and with coefficients of magnitude\(2^{\log ^{O(1)} n} \) and functionsh n :Z→{0,1} such that for eachn and eachx∈{0,1}n,XL (x) =h n (p n (x 1 ,...,x n )). This improves an earlier result of Yao (1985). We also analyze and improve modulus-amplifying polynomials constructed by Toda (1991) and Yao (1985).
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