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arXiv · 1801.04103

Self-Predicting Boolean Functions

Nir Weinberger·Ofer Shayevitz
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Abstract

A Boolean function $g$ is said to be an optimal predictor for another Boolean function $f$, if it minimizes the probability that $f(X^{n})\neq g(Y^{n})$ among all functions, where $X^{n}$ is uniform over the Hamming cube and $Y^{n}$ is obtained from $X^{n}$ by independently flipping each coordinate with probability $\delta$. This paper is about self-predicting functions, which are those that coincide with their optimal predictor.

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Nir Weinberger, Ofer Shayevitz. 2018-01-12. Self-Predicting Boolean Functions. https://arxiv.org/abs/1801.04103

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