computational complexity

, Volume 4, Issue 4, pp 350–366



  • Richard Beigel
    • Dept. of Computer ScienceUniversity of Yale
  • Jun Tarui
    • Department of Communications & Systems EngineeringUniversity of Electro-Communications

DOI: 10.1007/BF01263423

Cite this article as:
Beigel, R. & Tarui, J. Comput Complexity (1994) 4: 350. doi:10.1007/BF01263423


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 polynomialspn(x1,..., xn) overZ of degree logO(1)n and with coefficients of magnitude\(2^{\log ^{O(1)} n} \) and functionshn:Z→{0,1} such that for eachn and eachx∈{0,1}n,XL(x)=hn(pn(x1,...,xn)). 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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© Birkhäuser Verlag 1994