Are most Boolean functions determined by low frequencies?

Roman Vershynin

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arXiv · 2401.13143

Are most Boolean functions determined by low frequencies?

Roman Vershynin

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Abstract

We ask whether most Boolean functions are determined by their low frequencies. We show a partial result: for almost every function $f: \{-1,1\}^p \to \{-1,1\}$ there exists a function $f': \{-1,1\}^p \to (-1,1)$ that has the same frequencies as $f$ up to dimension $(1/2-o(1))p$.

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Roman Vershynin. 2024-12-20. Are most Boolean functions determined by low frequencies?. https://arxiv.org/abs/2401.13143

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