## Abstract

Nondeterministic communication protocols in which no input has too many witnesses are studied. Two different lower bounds are presented for n_{k}(f), defined as the minimum complexity of a nondeterministic protocol for the function f in which each input has at most k witnesses. One result shows that n_{k}(f) is bounded below by Ω(√c(f)/k) where c(f) is the deterministic complexity. A second result bounds n_{k}(f) by log(rk(M_{f}))/k-1, where rk(M_{f}) is the rank of the representing matrix of f. It follows that the communication complexity analogue of the Turing-complexity class FewP is equal to the analogue of the class P.

Original language | English |
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Title of host publication | Proceedings of the Seventh Annual Structure in Complexity Theory Conference |

Publisher | Publ by ERROR: no PUB record found for PX none CN nonpie IG 75516 |

Pages | 275-281 |

Number of pages | 7 |

ISBN (Print) | 081862955X |

State | Published - 1992 |

Externally published | Yes |

Event | Proceedings of the Seventh Annual Structure in Complexity Theory Conference - Boston, MA, USA Duration: 22 Jun 1992 → 25 Jun 1992 |

### Publication series

Name | Proceedings of the Seventh Annual Structure in Complexity Theory Conference |
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### Conference

Conference | Proceedings of the Seventh Annual Structure in Complexity Theory Conference |
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City | Boston, MA, USA |

Period | 22/06/92 → 25/06/92 |

### Bibliographical note

Funding Information:In the two-party communication complexity model, two parties compute a function that depends on both of their (initially private) inputs. Roughly speaking, the deterministic communication complexity of a function f(x, y) is the minimum * Supported by NSF Grant CCR90-10533. t This work was done while the author was at the Royal Instituut of Technology, Stockholm. Supported in part by NSF Grant CCR89-11388, and AFOSR Grants 89-0512B and 90-0008.

## ASJC Scopus subject areas

- Engineering (all)