## Abstract

We show that every language*L* 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 log^{O(1)}*n* at the leaves, or equivalently, there exist polynomials*p*_{ n }**(x**_{ 1 }**,..., x**_{ n }) over**Z** of degree log^{O(1)}*n* and with coefficients of magnitude\(2^{\log ^{O(1)} n} \) and functions*h*_{ n }:**Z**→{0,1} such that for each*n* and each*x*∈{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).

## Subject classifications

68Q05 68Q15 68Q25## Preview

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© Birkhäuser Verlag 1994