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

Zander Kelley; Shachar Lovett; Raghu Meka

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arXiv · 2308.12451

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

Zander Kelley·Shachar Lovett·Raghu Meka

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Abstract

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

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Zander Kelley, Shachar Lovett, Raghu Meka. 2023-08-23. Explicit separations between randomized and deterministic Number-on-Forehead communication. https://arxiv.org/abs/2308.12451

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