3 years ago

# Self-Predicting Boolean Functions.

Nir Weinberger, Ofer Shayevitz

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.

Publisher URL: http://arxiv.org/abs/1801.04103

DOI: arXiv:1801.04103v1

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