### Abstract

We show an exponential gap between communication complexity and external information complexity, by analyzing a communication task suggested as a candidate by Braverman. Previously, only a separation of communication complexity and internal information complexity was known. More precisely, we obtain an explicit example of a search problem with external information complexity ≤ O(k), with respect to any input distribution, and distributional communication complexity ≥ 2^{k}, with respect to some input distribution. In particular, this shows that a communication protocol cannot always be compressed to its external information. By a result of Braverman, our gap is the largest possible. Moreover, since the upper bound of O(k) on the external information complexity of the problem is obtained with respect to any input distribution, our result implies an exponential gap between communication complexity and information complexity (both internal and external) in the non-distributional setting of Braverman. In this setting, no gap was previously known, even for internal information complexity.

Original language | English (US) |
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Title of host publication | STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing |

Editors | Yishay Mansour, Daniel Wichs |

Publisher | Association for Computing Machinery |

Pages | 977-986 |

Number of pages | 10 |

ISBN (Electronic) | 9781450341325 |

DOIs | |

State | Published - Jun 19 2016 |

Externally published | Yes |

Event | 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016 - Cambridge, United States Duration: Jun 19 2016 → Jun 21 2016 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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Volume | 19-21-June-2016 |

ISSN (Print) | 0737-8017 |

### Other

Other | 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016 |
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Country | United States |

City | Cambridge |

Period | 6/19/16 → 6/21/16 |

### All Science Journal Classification (ASJC) codes

- Software

### Keywords

- Communication complexity
- Communication compression
- Information complexity

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## Cite this

*STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing*(pp. 977-986). (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. 19-21-June-2016). Association for Computing Machinery. https://doi.org/10.1145/2897518.2897535