New Separations Results for External Information

TL;DR

This paper establishes new exponential and quadratic separation results between external information complexity and other communication complexity measures for boolean functions, advancing understanding of information-theoretic limits in communication protocols.

Contribution

It proves the first exponential separation between external and internal information complexity and a near-quadratic separation between amortized zero-error communication and external information complexity.

Findings

Exponential separation between external and internal information complexity.

Near-quadratic separation between amortized zero-error communication and external information complexity.

Tight upper bound matching the exponential separation.

Abstract

We obtain new separation results for the two-party external information complexity of boolean functions. The external information complexity of a function $f(x,y)$ is the minimum amount of information a two-party protocol computing $f$ must reveal to an outside observer about the input. We obtain the following results: 1. We prove an exponential separation between external and internal information complexity, which is the best possible; previously no separation was known. 2. We prove a near-quadratic separation between amortized zero-error communication complexity and external information complexity for total functions, disproving a conjecture of \cite{Bravermansurvey}. 3. We prove a matching upper showing that our separation result is tight.