Self-Predicting Boolean Functions

01/12/2018

∙

by   Nir Weinberger, et al.

∙

0

∙

share

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)≠ 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 δ. This paper is about self-predicting functions, which are those that coincide with their optimal predictor.