Equality is Far Weaker than Constant-Cost Communication

Mika Göös; Nathaniel Harms; Artur Riazanov

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arXiv · 2507.11162

Equality is Far Weaker than Constant-Cost Communication

Mika Göös·Nathaniel Harms·Artur Riazanov

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Abstract

We exhibit an $n$-bit communication problem with a constant-cost randomized protocol but which requires $n^{\Omega(1)}$ deterministic (or even non-deterministic) queries to an Equality oracle. Therefore, even constant-cost randomized protocols cannot be efficiently "derandomized" using Equality oracles. This improves on several recent results and answers a question from the survey of Hatami and Hatami (SIGACT News 2024). It also gives a significantly simpler and quantitatively superior proof of the main result of Fang, G\"o\"os, Harms, and Hatami ( STOC 2025), that constant-cost communication does not reduce to the $k$-Hamming Distance hierarchy.

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BibTeX RIS

Mika Göös, Nathaniel Harms, Artur Riazanov. 2025-07-15. Equality is Far Weaker than Constant-Cost Communication. https://arxiv.org/abs/2507.11162

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