Sensitivity versus block sensitivity of Boolean functions

TL;DR

This paper constructs Boolean functions demonstrating a quadratic separation between sensitivity and block sensitivity, advancing understanding of their relationship in computational complexity.

Contribution

It introduces a new sequence of Boolean functions with a larger separation between sensitivity and block sensitivity than previously known.

Findings

Constructed Boolean functions with bs(f) = 1/2 s(f)^2 + 1/2 s(f)

Improved the known separation between sensitivity and block sensitivity

Performed computer searches for functions with up to 12 variables

Abstract

Determining the maximal separation between sensitivity and block sensitivity of Boolean functions is of interest for computational complexity theory. We construct a sequence of Boolean functions with bs(f) = 1/2 s(f)^2 + 1/2 s(f). The best known separation previously was bs(f) = 1/2 s(f)^2 due to Rubinstein. We also report results of computer search for functions with at most 12 variables.