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computational complexity

, Volume 4, Issue 4, pp 350–366 | Cite as

On ACC

  • Richard Beigel
  • Jun Tarui
Article

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).

Subject classifications

68Q05 68Q15 68Q25 

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Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • Richard Beigel
    • 1
  • Jun Tarui
    • 2
  1. 1.Dept. of Computer ScienceUniversity of YaleNew HavenU.S.A.
  2. 2.Department of Communications & Systems EngineeringUniversity of Electro-CommunicationsTokyoJapan

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