Information complexity is computable

TL;DR

This paper proves that the information complexity of any function is computable by providing an approximation algorithm with arbitrary precision, resolving a long-standing open question in information theory.

Contribution

It introduces the first algorithm to approximate the information complexity of functions to any desired accuracy, establishing its computability.

Findings

Provided an explicit approximation algorithm for information complexity.

Established an upper bound on convergence rate of restricted to unrestricted information complexity.

Resolved the open question of whether information complexity is computable.

Abstract

The information complexity of a function $f$ is the minimum amount of information Alice and Bob need to exchange to compute the function $f$. In this paper we provide an algorithm for approximating the information complexity of an arbitrary function $f$ to within any additive error $\alpha > 0$, thus resolving an open question as to whether information complexity is computable. In the process, we give the first explicit upper bound on the rate of convergence of the information complexity of $f$ when restricted to $b$-bit protocols to the (unrestricted) information complexity of $f$.