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We study the power of randomness in the Number-on-Forehead (NOF) model incommunication complexity. We construct an explicit 3-player function $f:[N]^3\to \{0,1\}$, such that: (i) there exist a randomized NOF protocol computing itthat sends a constant number of bits; but (ii) any deterministic ornondeterministic NOF protocol computing it requires sending about $(\logN)^{1/3}$ many bits. This exponentially improves upon the previously best-knownsuch separation. At the core of our proof is an extension of a recent result ofthe first and third authors on sets of integers without 3-term arithmeticprogressions into a non-arithmetic setting.

Explicit separations between randomized and deterministic Number-on-Forehead communication