On the resolution of the sensitivity conjecture

TL;DR

This paper surveys the resolution of the Sensitivity Conjecture in theoretical computer science, highlighting Hao Huang's proof and exploring influential ideas and future research directions in Boolean function complexity.

Contribution

It provides an exposition of key papers that inspired the proof of the Sensitivity Conjecture and discusses subsequent progress and research avenues.

Findings

Hao Huang's succinct proof of the Sensitivity Conjecture

Impactful ideas from four influential papers

Ongoing research directions in Boolean function complexity

Abstract

The Sensitivity Conjecture is a long-standing problem in theoretical computer science that seeks to fit the sensitivity of a Boolean function into a unified framework formed by the other complexity measures of Boolean functions, such as block sensitivity and certificate complexity. After more than thirty years of attacks on this Conjecture, Hao Huang (2019) gave a very succinct proof of the Conjecture. In this survey, we explore the ideas that inspired the proof of this Conjecture by an exposition of four papers that had the most impact on the Conjecture. We also discuss progress on further research directions that the Conjecture leads us to.