Abstract.We show that every language L in the class ACC can be recognized by depth-two deterministic circuits with a symmetricfunction gate at the root and 2 l~176 AND gates of fan-in log~ at the leaves, or equivalently~ there exist polynomials p~ (xl,.~ ,, x~) over Z of degree log~ and with coefficients of magnitude 2 l~176 and functions h,~ : Z ---, {0, 1} such that for each n and eo~ch x C {0, 1} n, XL(X) = h,.(p~(xt,...,xn)).This improves an earlier result of Yao (1985). We also analyze and improve modulus-amplifying polynomiMs constructed by Toda (1991) andYao (1985)i Subject classifications. 68Q05, 68Q15, 68Q25.

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