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The Courtade-Kumar Most Informative Boolean Function Conjecture and a Symmetrized Li-M\'edard Conjecture are Equivalent
- Publication Year :
- 2020
-
Abstract
- We consider the Courtade-Kumar most informative Boolean function conjecture for balanced functions, as well as a conjecture by Li and M\'edard that dictatorship functions also maximize the $L^\alpha$ norm of $T_pf$ for $1\leq\alpha\leq2$ where $T_p$ is the noise operator and $f$ is a balanced Boolean function. By using a result due to Laguerre from the 1880's, we are able to bound how many times an $L^\alpha$-norm related quantity can cross zero as a function of $\alpha$, and show that these two conjectures are essentially equivalent.
- Subjects :
- Computer Science - Information Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2004.01277
- Document Type :
- Working Paper