Making randomness public in unbounded-round information complexity

Abstract

We prove a version of a “Reverse Newman Theorem” in information complexity: every private-coin communication protocol with information complexity I and communication complexity C can be converted into a public-coin protocol with the same behavior so that it’s information complexity does not exceed O(Formula Presented). “Same behavior” means that the transcripts of these two protocols are identically distributed on each pair of inputs. Such a conversion was previously known only for one-way protocols. Our result provides a new proof for the best-known compression theorem in Information Complexity.