Exponential Separation of Information and Communication
Ran Raz, Professor, Mathematics and Computer Science, Weizmann Institute
Date: Monday, November 24, 2014
Time: 4:15 PM to 5:15 PM Note: all times are in the Eastern Time Zone
Refreshments: 3:45 PM
Location: Patil/Kiva G449
Host: Costis Daskalakis, Ankur Moitra, Dana Moshkovitz and Vinod Vaikuntanathan
Contact: Deborah Lehto, 617.324.7303, email@example.com
Speaker URL: None
TALK: Ran Raz, Professor, Mathematics and Computer Science, Weizmann Institute: Exponential Separation of Information and Communication
Abstract: In profoundly influential works, Shannon and Huffman show that if Alice wants to send a message X to Bob, it's sufficient for her to send roughly H(X) bits (in expectation), where H denotes Shannon's entropy function. In other words, the message x can be compressed to roughly H(X) bits, the information content of the message. Can one prove similar results in the interactive setting, where Alice and Bob engage in an interactive communication protocol?
We show the first gap between communication complexity and information complexity, by giving an explicit example of a partial boolean function with information complexity O(k), and distributional communication complexity > 2^k. This shows that a communication protocol cannot always be compressed to its internal information, answering (the standard formulation of) the above question in the negative. By a result of Braverman, our example gives the largest possible gap.
By a result of Braverman and Rao, our example gives the first gap between communication complexity and amortized communication complexity, implying that strong direct sum does not hold for distributional communication complexity.
Joint work with Anat Ganor and Gillat Kol.
Created by Deborah Goodwin at Monday, November 24, 2014 at 10:29 AM.