Exponential separation of information and communication for boolean functions

Anat Ganor, Gillat Kol, Ran Raz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We show an exponential gap between communication complexity and information complexity for boolean functions, by giving an explicit example of a partial function with information complexity ≤ O(k), and distributional communication complexity ≥ 2k. This shows that a communication protocol for a partial boolean function cannot always be compressed to its internal information. By a result of Braverman [3], our gap is the largest possible. By a result of Braverman and Rao [4], our example shows a gap between communication complexity and amortized communication complexity, implying that a tight direct sum result for distributional communication complexity of boolean functions cannot hold, answering a long standing open problem. Our techniques build on [13], that proved a similar result for relations with very long outputs (double exponentially long in k). In addition to the stronger result, the current work gives a simpler proof, benefiting from the short output length of boolean functions. Another (conceptual) contribution of our work is the relative discrepancy method, a new rectangle-based method for proving communication complexity lower bounds for boolean functions, powerful enough to separate information complexity and communication complexity.

Original languageEnglish
Title of host publicationSTOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Pages557-566
Number of pages10
ISBN (Electronic)9781450335362
DOIs
StatePublished - 14 Jun 2015
Externally publishedYes
Event47th Annual ACM Symposium on Theory of Computing, STOC 2015 - Portland, United States
Duration: 14 Jun 201517 Jun 2015

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
Volume14-17-June-2015
ISSN (Print)0737-8017

Conference

Conference47th Annual ACM Symposium on Theory of Computing, STOC 2015
Country/TerritoryUnited States
CityPortland
Period14/06/1517/06/15

Keywords

  • Amortized communication complexity
  • Communication complexity
  • Communication compression
  • Direct sum
  • Information complexity

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