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How small can be a layered boolean circuit for a function with circuit complexity $s$?

$O(s\cdot \log s)$, or $O(s)$), or for interesting class of circuits? Background. … $s/\log s$ or $s/\log\log s)$; I'm trying to understand how restrictive this restriction to layered boolean circuits can be in practice, either for general circuits or for "natural" circuits. …
Geoffroy Couteau's user avatar