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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 Dependency relation ： ウィキペディア英語版 Dependency relation In mathematics and computer science, a dependency relation is a binary relation that is finite, symmetric, and reflexive; i.e. a finite tolerance relation. That is, it is a finite set of ordered pairs $D$, such that * If $(a,b)\backslash in\; D$ then $(b,a)\; \backslash in\; D$ (symmetric) * If $a$ is an element of the set on which the relation is defined, then $(a,a)\; \backslash in\; D$ (reflexive) In general, dependency relations are not transitive; thus, they generalize the notion of an equivalence relation by discarding transitivity. Let $\backslash Sigma$ denote the alphabet of all the letters of $D$. Then the independency induced by $D$ is the binary relation $I$ :$I\; =\; \backslash Sigma\; \backslash times\; \backslash Sigma\; \backslash setminus\; D$ That is, the independency is the set of all ordered pairs that are not in $D$. The independency is symmetric and irreflexive. The pairs $(\backslash Sigma,\; D)$ and $(\backslash Sigma,\; I)$, or the triple $(\backslash Sigma,\; D,\; I)$ (with $I$ induced by $D$) are sometimes called the concurrent alphabet or the reliance alphabet. The pairs of letters in an independency relation induce an equivalence relation on the free monoid of all possible strings of finite length. The elements of the equivalence classes induced by the independency are called traces, and are studied in trace theory. ==Examples== Consider the alphabet $\backslash Sigma=\backslash$. A possible dependency relation is : $$ \begin D &= \\times\ \quad \cup \quad \\times\ \\ &= \^2 \cup \^2 \\ &= \ \end The corresponding independency is :$I\_D=\backslash$ Therefore, the letters $b,c$ commute, or are independent of one another. 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「Dependency relation」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.