|Time+Place:||Monday 05/01/2015 14:30 Room Class 6, Floor 1, Taub Bld.|
|Title:||Exponential Separation of Information and Communication|
|Speaker:|| Gillat Kol- CS-Lecture - NOTE UNUSUAL DAY AND ROOM
|| Affiliation: || Institute for Advanced Study (IAS), Princeton
|| Host: || Keren Censor-Hillel
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 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, answering a long standing open problem. Joint work with Anat Ganor and Ran Raz. Short Bio: I am a postdoc fellow in the theoretical computer science group at the Institute for Advanced Study (IAS), Princeton. My research is in complexity theory. I am currently very interested in application of information theory to theoretical computer science, especially to communication complexity. Prior to joining the IAS, I completed a short postdoc at the Technion, received a Ph.d. and M.Sc. from the Weizmann Institute, and a B.A. from the Open University of Israel.