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Extractor Biography

This article is about the extractor in mathematics, for other usage of this word see: extractor . An (N,M,D,K,epsilon) -extractor is a bipartite graph with N nodes on the left and M nodes on the right such that each node on the left has D neighbors (on the right), which has the added property thatfor any subset A of the left vertices of size at least K, the distribution on right vertices obtained by choosing a random node in A and then following a random edge to get a node x on the right side is epsilon-close to the uniform distribution in terms of total variation distance.A disperser is a related graph.An equivalent way to view an extractor is as a bivariate function E : [1] times [2] rightarrow [3] in the natural way. With this view it turns out that the extractor property is equivalent to: for any source of randomness X that gives n bits with min-entropy log K, the distribution E(X,U_D) is epsilon-close to U_M, where U_T denotes the uniform distribution on [4].Extractors are in

Source: http://en.wikipedia.org/wiki/eXtractor
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