Self-predicting boolean functions

Nir Weinberger, Ofer Shayevitz

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)665-693
Number of pages29
JournalSIAM Journal on Discrete Mathematics
Volume33
Issue number2
DOIs
StatePublished - 2019

Funding

FundersFunder number
Horizon 2020 Framework Programme639573
European Research Council

    Keywords

    • Boolean functions
    • Fourier analysis
    • Optimal prediction
    • Stability

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