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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Extractor (mathematics) ： ウィキペディア英語版 Extractor (mathematics) An $(N,M,D,K,\backslash epsilon)$ -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 that for 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 $\backslash epsilon$-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 :$E\; :\; ()\; \backslash times\; ()\; \backslash rightarrow\; ()$ 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 $\backslash log\; K$, the distribution $E(X,U\_D)$ is $\backslash epsilon$-close to $U\_M$, where $U\_T$ denotes the uniform distribution on $()$. Extractors are interesting when they can be constructed with small $K,D,\backslash epsilon$ relative to $N$ and $M$ is as close to $KD$ (the total randomness in the input sources) as possible. Extractor functions were originally researched as a way to ''extract'' randomness from weakly random sources. ''See'' randomness extractor. Using the probabilistic method it is easy to show that extractor graphs with really good parameters exist. The challenge is to find explicit or polynomial time computable examples of such graphs with good parameters. Algorithms that compute extractor (and disperser) graphs have found many applications in computer science. ==References== * Ronen Shaltiel, (Recent developments in extractors ) - a survey 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Extractor (mathematics)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.