Top-Down Lower Bounds for Depth-Four Circuits

Mika Göös; Artur Riazanov; Anastasia Sofronova; Dmitry Sokolov

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arXiv · 2304.02555

Top-Down Lower Bounds for Depth-Four Circuits

Mika Göös·Artur Riazanov·Anastasia Sofronova·Dmitry Sokolov

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Abstract

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.

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Mika Göös, Artur Riazanov, Anastasia Sofronova, Dmitry Sokolov. 2023-04-05. Top-Down Lower Bounds for Depth-Four Circuits. https://arxiv.org/abs/2304.02555

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