2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218226In this paper, we show that for every constant $0 < ε< 1/2$ and for every constant $d \geq 2$, the minimum size of a depth $d$ Boolean circuit that $ε$-approximates Majority function on $n$ variables is exp$(Θ(n^{1/(2d-2)}))$. The lower bound for every $d \geq 2$ 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 $d \geq 3$.12 pagesComputational Complexitytext