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Abstract

This paper provides the first general technique for proving information lower bounds on two-party unbounded-rounds communication problems. We show that the discrepancy lower bound, which applies to randomized communication complexity, also applies to information complexity. More precisely, if the discrepancy of a two-party function f with respect to a distribution μ is Disc μ f, then any two party randomized protocol computing f must reveal at least Ω(log(1/Disc μ f)) bits of information to the participants. As a corollary, we obtain that any two-party protocol for computing a random function on {0,1} n ×{0,1} n must reveal Ω(n) bits of information to the participants.

In addition, we prove that the discrepancy of the Greater-Than function is \(\Omega(1/\sqrt{n})\), which provides an alternative proof to the recent proof of Viola [Vio11] of the Ω(logn) lower bound on the communication complexity of this well-studied function and, combined with our main result, proves the tight Ω(logn) lower bound on its information complexity.

The proof of our main result develops a new simulation procedure that may be of an independent interest. In a very recent breakthrough work of Kerenidis et al. [KLL+12], this simulation procedure was a building block towards a proof that almost all known lower bound techniques for communication complexity (and not just discrepancy) apply to information complexity.

Keywords

Mutual Information Success Probability Communication Complexity Information Cost Information Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mark Braverman
    • 1
    • 2
  • Omri Weinstein
    • 2
  1. 1.University of TorontoCanada
  2. 2.Princeton UniversityUSA

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