## Abstract

We study non-deterministic communication protocols in which no input has too many witnesses. Define n_{k}(f) to be the minimum complexity of a non-deterministic protocol for the function f in which each input has at most k witnesses. We present two different lower bounds for n_{k}(f). Our first result shows that n_{k}(f) is below by Ω(√c(f)/k), where c(f) is the deterministic complexity. Our second results bounds n_{k}(f) by log(rk(M_{f}))/k - 1, where rk(M_{f}) is the rank of the representing matrix of f. As a consequence, 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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Pages (from-to) | 247-257 |

Number of pages | 11 |

Journal | Journal of Computer and System Sciences |

Volume | 49 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1994 |

### 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

- Theoretical Computer Science
- General Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics