Bounds on the Size of Small Depth Circuits for Approximating Majority

  • Kazuyuki Amano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5555)


In this paper, we show that for every constant 0 < ε< 1/2 and for every constant d ≥ 2, the minimum size of a depth d Boolean circuit that ε-approximates Majority function on n variables is exp(Θ(n1/(2d − 2))). The lower bound for every d ≥ 2 and the upper bound for d = 2 have been previously shown by O’Donnell and Wimmer [ICALP’07], and the contribution of this paper is to give a matching upper bound for d ≥ 3.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Kazuyuki Amano
    • 1
  1. 1.Dept of Comput SciGunma Univ.GunmaJapan

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