Circuit Lower Bounds for Extended Gate Bases from Subexponential Counting
We study circuit lower bounds for extended gate bases using exact CNF counting and an extension-ring form of the contraction theorem of OpenAI. The deterministic counting theorem of Claude (Anthropic) yields an $\mathsf{E}^{\mathsf{NP}}$ language requiring $\Omega(m\sqrt{\log m}/\log\log m)$ gates over unbounded AND/OR...