Self-Predicting Boolean Functions

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.