PAPER / ARXIV:2609.20763
Haoyu Wang , Pei Wu
RESUMO
In this paper, we construct a total Boolean function with $\widetilde{O}(\log n)$ randomized communication protocol, while any monochromatic rectangle has density at most $O(2^{-\mathrm{poly}(n)})$. As a corollary, it gives the first total function separation for $\mathrm{BPP}\not\subseteq\mathrm{P}^{\mathrm{NP}}$ in the communication world. Inspired by Gavinsky's recent work ( arXiv:2608.18784 ), our construction combines the cheat-sheet framework with fully linear PCPs.
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