### Abstract

We obtain a strong direct product theorem for two-party bounded round communication complexity. Let suc_{r} (μ, f, C) denote the maximum success probability of an r-round communication protocol that uses at most C bits of communication in computing f(x,y) when (x,y) ∼ μ. Jain et al. [12] have recently showed that if suc_{r}(μ, f, C) ≤ 2/3 and T ≪, (C - Ω(r^{2}))·n/r, then suc^{r}(μ ^{n}, f^{n}, T) ≤ exp(-Ω(n/r^{2})). Here we prove that if suc_{7r}(μ, f, C) ≤ 2/3 and T ≪ (C - Ω(r log r))·n then suc_{r}(μ^{n}, f^{n}, T) ≤ exp(-Ω(n)). Up to a log r factor, our result asymptotically matches the upper bound on suc_{7r} (μ^{n} ,f^{n}, T) given by the trivial solution which applies the per-copy optimal protocol independently to each coordinate. The proof relies on a compression scheme that improves the tradeoff between the number of rounds and the communication complexity over known compression schemes.

Original language | English (US) |
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Title of host publication | Automata, Languages, and Programming - 40th International Colloquium, ICALP 2013, Proceedings |

Pages | 232-243 |

Number of pages | 12 |

Edition | PART 1 |

DOIs | |

State | Published - Jul 23 2013 |

Event | 40th International Colloquium on Automata, Languages, and Programming, ICALP 2013 - Riga, Latvia Duration: Jul 8 2013 → Jul 12 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 1 |

Volume | 7965 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 40th International Colloquium on Automata, Languages, and Programming, ICALP 2013 |
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Country | Latvia |

City | Riga |

Period | 7/8/13 → 7/12/13 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Automata, Languages, and Programming - 40th International Colloquium, ICALP 2013, Proceedings*(PART 1 ed., pp. 232-243). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7965 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-39206-1_20