computational complexity

, Volume 4, Issue 4, pp 350-366

First online:


  • Richard BeigelAffiliated withDept. of Computer Science, University of Yale
  • , Jun TaruiAffiliated withDepartment of Communications & Systems Engineering, University of Electro-Communications

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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 log O(1) n at the leaves, or equivalently, there exist polynomialsp n (x 1 ,..., x n ) overZ of degree log O(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).

Subject classifications

68Q05 68Q15 68Q25