Document Type
Article
Publication Date
11-2016
Published In
Algorithmica
Abstract
Newman’s theorem states that we can take any public-coin communication protocol and convert it into one that uses only private randomness with but a little increase in communication complexity. We consider a reversed scenario in the context of information complexity: can we take a protocol that uses private randomness and convert it into one that only uses public randomness while preserving the information revealed to each player? We prove that the answer is yes, at least for protocols that use a bounded number of rounds. As an application, we prove new direct-sum theorems through the compression of interactive communication in the bounded-round setting. To obtain this application, we prove a new one-shot variant of the Slepian–Wolf coding theorem, interesting in its own right. Furthermore, we show that if a Reverse Newman’s Theorem can be proven in full generality, then full compression of interactive communication and fully-general direct-sum theorems will result.
Keywords
Communication complexity, Information complexity, Information theory, Compression, Slepian–Wolf
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Joshua Brody, H. Buhrman, M. Koucký, B. Loff, F. Speelman, and N. Vereshchagin.
(2016).
"Towards A Reverse Newman’s Theorem In Interactive Information Complexity".
Algorithmica.
Volume 76,
Issue 3.
749-781.
DOI: 10.1007/s00453-015-0112-9
https://works.swarthmore.edu/fac-comp-sci/38
Comments
This paper was previously presented the 2013 IEEE Conference on Computational Complexity (CCC); this previous version is freely available online courtesy of the author.