Self-predicting boolean functions

Nir Weinberger; Ofer Shayevitz

doi:10.1137/18M1207119

Self-predicting boolean functions

Nir Weinberger, Ofer Shayevitz

School of Electrical Engineering

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
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

Funding

Funders	Funder number
European Research Council
Horizon 2020 Framework Programme	639573

Keywords

Boolean functions
Fourier analysis
Optimal prediction
Stability

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10.1137/18M1207119

Cite this

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Self-predicting boolean functions

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