Self-predicting boolean functions

Nir Weinberger; Ofer Shayevitz

doi:10.1137/18M1207119

Self-predicting boolean functions

School of Electrical Engineering

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

A Boolean function g is said to be an optimal predictor for another Boolean function f if it minimizes the probability that f(Xⁿ) = g(Y ⁿ) among all functions, where Xⁿ is uniform over the Hamming cube and Y ⁿ is obtained from Xⁿ by independently flipping each coordinate with probability δ. This paper is about self-predicting functions, which are those that coincide with their optimal predictor.

Original language	English GB
Pages (from-to)	665-693
Number of pages	29
Journal	SIAM Journal on Discrete Mathematics
Volume	33
Issue number	2
DOIs	https://doi.org/10.1137/18M1207119
State	Published - 2019

Keywords

Boolean functions
Fourier analysis
Optimal prediction
Stability

ASJC Scopus subject areas

General Mathematics

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10.1137/18M1207119

Cite this

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abstract = "A Boolean function g is said to be an optimal predictor for another Boolean function f if it minimizes the probability that f(Xn) = g(Y n) among all functions, where Xn is uniform over the Hamming cube and Y n is obtained from Xn by independently flipping each coordinate with probability δ. This paper is about self-predicting functions, which are those that coincide with their optimal predictor.",

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KW - Fourier analysis

KW - Optimal prediction

KW - Stability

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Self-predicting boolean functions

Abstract

Keywords

ASJC Scopus subject areas

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