We present a top-down lower-bound method for depth-$4$ boolean circuits. In particular, we give a new proof of the well-known result that the parity function requires depth-$4$ circuits of size exponential in $n^{1/3}$. Our proof is an application of robust sunflowers and block unpredictability.
翻译:我们提出了一种深度为4的布尔电路的自上而下下界方法。具体而言,我们给出了一个众所周知的结论的新证明,即奇偶校验函数需要规模为$n^{1/3}$指数级的深度4电路。我们的证明运用了鲁棒向日葵和块不可预测性。