Self-Predicting Boolean Functions

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

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