English

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

Computational Complexity 2024-01-19 v2

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 128/452.8444128/45 \approx 2.8444 which is presently the highest known value of this ratio that is achieved by any Boolean function. Correspondingly, 128/45128/45 is also presently the best known lower bound on the universal constant of the Fourier min-entropy/influence conjecture.

Keywords

Cite

@article{arxiv.2212.07713,
  title  = {A Lower Bound on the Constant in the Fourier Min-Entropy/Influence Conjecture},
  author = {Aniruddha Biswas and Palash Sarkar},
  journal= {arXiv preprint arXiv:2212.07713},
  year   = {2024}
}