The Courtade-Kumar Most Informative Boolean Function Conjecture and a Symmetrized Li-Médard Conjecture are Equivalent
| Autor: | Ayfer Ozgur, Leighton Pate Barnes |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Combinatorics
Conjecture Computer Science - Information Theory Norm (mathematics) 0202 electrical engineering electronic engineering information engineering Balanced boolean function Laguerre polynomials 020206 networking & telecommunications 02 engineering and technology Boolean function Mathematics |
| Zdroj: | ISIT |
| DOI: | 10.1109/isit44484.2020.9174063 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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