### Abstract

We describe new ways to simulate 2-party communication protocols to get protocols with potentially smaller communication. We show that every communication protocol that communicates C bits and reveals I bits of information about the inputs to the participating parties can be simulated by a new protocol involving at most Õ(√CI) bits of communication. If the protocol reveals I bits of information about the inputs to an observer that watches the communication in the protocol, we show how to carry out the simulation with Õ(I) bits of communication. These results lead to a direct sum theorem for randomized communication complexity. Ignoring polylogarithmic factors, we show that for worst case computation, computing n copies of a function requires √n times the communication required for computing one copy of the function. For average case complexity, given any distribution μ on inputs, computing n copies of the function on n inputs sampled independently according to μ requires √n times the communication for computing one copy. If μ is a product distribution, computing n copies on n independent inputs sampled according to μ requires n times the communication required for computing the function. We also study the complexity of computing the sum (or parity) of n evaluations of f, and obtain results analogous to those above.

Original language | English (US) |
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Title of host publication | STOC'10 - Proceedings of the 2010 ACM International Symposium on Theory of Computing |

Pages | 67-76 |

Number of pages | 10 |

DOIs | |

State | Published - Jul 23 2010 |

Externally published | Yes |

Event | 42nd ACM Symposium on Theory of Computing, STOC 2010 - Cambridge, MA, United States Duration: Jun 5 2010 → Jun 8 2010 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0737-8017 |

### Other

Other | 42nd ACM Symposium on Theory of Computing, STOC 2010 |
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Country | United States |

City | Cambridge, MA |

Period | 6/5/10 → 6/8/10 |

### All Science Journal Classification (ASJC) codes

- Software

### Keywords

- communication complexity
- compression
- direct sum
- information theory

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## Cite this

*STOC'10 - Proceedings of the 2010 ACM International Symposium on Theory of Computing*(pp. 67-76). (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/1806689.1806701