SelfPredicting Boolean Functions
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 selfpredicting functions, which are those that coincide with their optimal predictor.
 Publication:

arXiv eprints
 Pub Date:
 January 2018
 DOI:
 10.48550/arXiv.1801.04103
 arXiv:
 arXiv:1801.04103
 Bibcode:
 2018arXiv180104103W
 Keywords:

 Computer Science  Discrete Mathematics;
 Computer Science  Information Theory;
 Mathematics  Combinatorics;
 Mathematics  Probability