UNSPECIFIED (1998) Explicit OR-dispersers with polylogarithmic degree. In: 27th Annual ACM Symposium on Theory of Computing, MAY 29-JUN 01, 1995, LAS VEGAS, NEVADA.

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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

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