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arXiv · 2308.00509

On the Analysis of Boolean Functions and Fourier-Entropy-Influence Conjecture

Xiao Han
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Abstract

This manuscript includes some classical results we select apart from the new results we've found on the Analysis of Boolean Functions and Fourier-Entropy-Influence conjecture. We try to ensure the self-completeness of this work so that readers could probably read it independently. Among the new results, what is the most remarkable is that we prove that the entropy of a boolean function $f$ could be upper bounded by $O(I(f))+O(\sum\limits_{k}I_k(f)\log (1/I_k(f)))$.

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Xiao Han. 2023-11-20. On the Analysis of Boolean Functions and Fourier-Entropy-Influence Conjecture. https://arxiv.org/abs/2308.00509

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