We give a $3.5n-o(n)$ lower bound on the size of Boolean circuits over the $B_2$ basis computing an explicit Boolean function F in P. This improves the best previous lower bound of $3.1n-o(n)$ [Li-Yang22].

The proof of the lower bound uses the gate elimination technique, and builds heavily on ideas ... more >>>

Michael O. Rabin was a major founder and leader of theoretical computer science. He died on April 14, 2026, at the age of 94. This paper aims to survey the wide scope and lasting impact of his research.

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We give a simplified, self-contained proof of OpenAI's parity lower bound for constant-depth quantum circuits with arbitrary one-qubit gates, unbounded-arity Toffoli gates, and polynomially many ancillas. The proof establishes product-projection localization and uses it to bound the parity Fourier coefficient of the acceptance probability. We remove one circuit layer directly, ... more >>>