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Revision #1 to TR22-180 | 17th January 2024 12:58

A Lower Bound on the Constant in the Fourier Min-Entropy/Influence Conjecture

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Revision #1
Authors: Aniruddha Biswas, Palash Sarkar
Accepted on: 17th January 2024 12:58
Downloads: 56
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Abstract:

We describe a new construction of Boolean functions. A specific instance of our construction provides a 30-variable Boolean function having min-entropy/influence ratio to be 128/45 ? 2.8444 which is presently the highest known value of this ratio that is achieved by any Boolean function. Correspondingly, 128/45 is also presently the best known lower bound on the universal constant of the Fourier min-entropy/influence conjecture.


Paper:

TR22-180 | 15th December 2022 12:09

A Lower Bound on the Constant in the Fourier Min-Entropy/Influence Conjecture


Abstract:

We describe a new construction of Boolean functions. A specific instance of our construction provides a 30-variable Boolean function having min-entropy/influence ratio to be 128/45 ? 2.8444 which is presently the highest known value of this ratio that is achieved by any Boolean function. Correspondingly, 128/45 is also presently the best known lower bound on the universal constant of the Fourier min-entropy/influence conjecture.



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