Exponential Separation of Information and Communication for Boolean Functions

@article{Ganor2014ExponentialSO,
  title={Exponential Separation of Information and Communication for Boolean Functions},
  author={Anat Ganor and Gillat Kol and Ran Raz},
  journal={Proceedings of the forty-seventh annual ACM symposium on Theory of Computing},
  year={2014}
}
  • A. Ganor, Gillat Kol, R. Raz
  • Published 14 June 2015
  • Computer Science
  • Proceedings of the forty-seventh annual ACM symposium on Theory of Computing
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 [Bra12], our gap is the largest possible. By a result of Braverman and Rao [BR11], our example… 

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