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### Explicit OR-dispersers with polylogarithmic degree

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UNSPECIFIED
(1998)
*Explicit OR-dispersers with polylogarithmic degree.*
In: 27th Annual ACM Symposium on Theory of Computing, LAS VEGAS, NEVADA, MAY 29-JUN 01, 1995. Published in: JOURNAL OF THE ACM, 45
(1). pp. 123-154.

**Full text not available from this repository.**

## Abstract

An (N, M, T)-OR-disperser is a bipartite multigraph G = (V, W, E) with \V\ = N, and \W\ = M, having the following expansion property: any subset of V having at least T vertices has a neighbor set of size at least M/2. For any pair of constants xi, lambda, 1 greater than or equal to xi > lambda greater than or equal to 0, any sufficiently large N, and for any T greater than or equal to 2((log N)xi), M less than or equal to 2((log N))(lambda), we give an explicit elementary construction of an (N, M, T)-OR-disperser such that the out-degree of any vertex in V is at most polylogarithmic in N. Using this with known applications of OR-dispersers yields several results. First, our construction implies that the complexity class Strong-RP defined by Sipser, equals RP. Second, for any fixed eta > 0, we give the first polynomial-time simulation of RP algorithms using the output of any "eta-minimally random" source. For any integral R > 0, such a source accepts a single request for an R-bit string and generates the string according to a distribution that assigns probability at most 2(-R eta) to any string. It is minimally random in the sense that any weaker source is insufficient to do a black-box polynomial-time simulation of RP algorithms.

Item Type: | Conference Item (UNSPECIFIED) |
---|---|

Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |

Journal or Publication Title: | JOURNAL OF THE ACM |

Publisher: | ASSOC COMPUTING MACHINERY |

ISSN: | 0004-5411 |

Date: | January 1998 |

Volume: | 45 |

Number: | 1 |

Number of Pages: | 32 |

Page Range: | pp. 123-154 |

Publication Status: | Published |

Title of Event: | 27th Annual ACM Symposium on Theory of Computing |

Location of Event: | LAS VEGAS, NEVADA |

Date(s) of Event: | MAY 29-JUN 01, 1995 |

URI: | http://wrap.warwick.ac.uk/id/eprint/15830 |

Data sourced from Thomson Reuters' Web of Knowledge

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