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On the Probabilistic Degree of an n-variate Boolean Function
[article]

2021
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arXiv
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pre-print

Nisan and Szegedy (CC 1994) showed that any Boolean function f:{0,1}^n→{0,1} that depends on all its input variables, when represented as a real-valued multivariate polynomial P(x_1,...,x_n), has degree at least log n - O(loglog n). This was improved to a tight (log n - O(1)) bound by Chiarelli, Hatami and Saks (Combinatorica 2020). Similar statements are also known for other Boolean function complexity measures such as Sensitivity (Simon (FCT 1983)), Quantum query complexity, and Approximate

arXiv:2107.03171v1
fatcat:2vfnlnbhfbcdhbt5dv3xzsn2eu