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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 rational set ： ウィキペディア英語版 rational set In computer science, more precisely in automata theory, a rational set of a monoid is an element of the minimal class of subsets of this monoid which contains all finite subsets and is closed under union, product and Kleene star. Rational sets are useful in automata theory, formal languages and algebra. A rational set generalizes the notion of rational (regular) language (understood as defined by regular expressions) to monoids that are not necessarily free. ==Definition== Let $N$ be a monoid. The set $\backslash mathrm(N)$ of rational subsets of $N$ is the smallest set that contains every finite set and is closed under * union: if $A,B\backslash in\; \backslash mathrm(N)$ then $A\backslash cup\; B\backslash in\; \backslash mathrm(N)$ * product: if $A,B\backslash in\; \backslash mathrm(N)$ then $A\backslash times\; B=\backslash \backslash in\backslash mathrm(N)$ * Kleene star if $A\backslash in\; \backslash mathrm(N)$ then $A^$ *=\bigcup_^\infty A^i \in\mathrm(N) where $A^1=A$ and $A^=A^n\backslash times\; A$. This means that any rational subset of $N$ can be obtained by taking a finite number of finite subsets of $N$ and applying the union, product and Kleene star operations a finite number of times. In general a rational subset of a monoid is not a submonoid. 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「rational set」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.