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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 Randomness merger ： ウィキペディア英語版 Randomness merger In extractor theory, a randomness merger is a function which extracts randomness out of a set of random variables, provided that at least one of them is uniformly random. Its name stems from the fact that it can be seen as a procedure which "merges" all the variables into one, preserving at least some of the entropy contained in the uniformly random variable. Mergers are currently used in order to explicitly construct randomness extractors. ==Intuition and definition== Consider a set of $k$ random variables, $X\_1,\backslash ldots,X\_k$, each distributed over $\backslash ^n$ at least one of which is uniformly random; but it is not known which one. Furthermore, the variables may be arbitrarily correlated: they may be functions of one another, they may be constant, and so on. However, since at least one of them is uniform, the set as a whole contains at least $n$ bits of entropy. The job of the merger is to output a new random variable, also distributed over $\backslash ^n$, that retains as much of that entropy as possible. Ideally, if it were known which of the variables is uniform, it could be used as the output, but that information is not known. The idea behind mergers is that by using a small additional random seed, it is possible to get a good result even without knowing which one is the uniform variable. Definition (merger): A function $M\; :\; (\backslash ^n)^k\; \backslash times\; \backslash ^d\; \backslash rightarrow\; \backslash ^n$ is called an $(m,\backslash varepsilon)$-merger if for every set of random variables $(X\_1,\backslash ldots,X\_k)$ distributed over $\backslash ^n$, at least one of which is uniform, the distribution of $Z\; =\; M(X\_1,\backslash ldots,X\_k,\; U\_d)$ has smooth min-entropy $H\_\backslash infty^\backslash varepsilon(Z)\; \backslash geq\; m$. The variable $U\_d$ denotes the uniform distribution over $d$ bits, and represents a truly random seed. In other words, by using a small uniform seed of length $d$, the merger returns a string which is $\backslash varepsilon$-close to having at least $m$ min-entropy; this means that its statistical distance from a string with $m$ min-entropy is no larger than $\backslash varepsilon$. Reminder: There are several notions of measuring the randomness of a distribution; the min-entropy of a random variable $Z$ is defined as the largest $k$ such that the most probable value of $Z$ occurs with probability no more than $2^$. The min-entropy of a string is an upper bound to the amount of randomness that can be extracted from it. 〔(【引用サイトリンク】title=Trevisan's extractor in the presence of quantum side information ) Section 2.2.〕 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「Randomness merger」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.