OpenAI research collection · 1 manuscript · Source checked 2026-10-19
Constructs a single language in deterministic polynomial time whose n-bit membership function requires 2^{ω(\sqrt n)} total gates in unbounded-fan-in OR–AND–OR circuits, at every sufficiently large input length. This crosses the square-root-exponent threshold for explicit depth-three Boolean circuit lower bounds.
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We construct a language in deterministic polynomial time whose n-bit membership function requires 2^{ω(\sqrt n)} gates in an unbounded-fan-in OR–AND–OR circuit. The bound holds at every sufficiently large input length and counts all gates, including the bottom layer.
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