Information Complexity and the Quest for Interactive Compression (A Survey)

TL;DR

This survey explores information complexity as a key tool in understanding communication and circuit complexity, highlighting recent advances in interactive protocol compression and fundamental conjectures.

Contribution

It provides an overview of recent progress in information complexity, especially its role in proving lower bounds and addressing core conjectures in communication and circuit complexity.

Findings

Breakthroughs in understanding direct sum and direct product conjectures

Advances in compressing interactive protocols

Deepened understanding of information complexity's applications

Abstract

Information complexity is the interactive analogue of Shannon's classical information theory. In recent years this field has emerged as a powerful tool for proving strong communication lower bounds, and for addressing some of the major open problems in communication complexity and circuit complexity. A notable achievement of information complexity is the breakthrough in understanding of the fundamental direct sum and direct product conjectures, which aim to quantify the power of parallel computation. This survey provides a brief introduction to information complexity, and overviews some of the recent progress on these conjectures and their tight relationship with the fascinating problem of compressing interactive protocols.