Separation Results for Boolean Function Classes

TL;DR

This paper demonstrates near-separations between key classes of Boolean functions using influence measures, bridging concepts from coding theory, cryptography, combinatorics, and complexity theory.

Contribution

It introduces a novel influence-based technique to distinguish Boolean function classes, achieving near-separations across multiple theoretical domains.

Findings

Influence measures differentiate Boolean function classes

Near-separation results between coding/cryptography and combinatorics classes

Technique applicable to various Boolean function classes

Abstract

We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In particular, we show (almost) separation of several classes of Boolean functions which have been studied in the coding theory and cryptography from classes which have been studied in combinatorics and complexity theory.