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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 Star height ： ウィキペディア英語版 Star height In theoretical computer science, more precisely in the theory of formal languages, the star height is a measure for the structural complexity of regular expressions: The star height equals the maximum nesting depth of stars appearing in the regular expression. The concept of star height was first defined and studied by Eggan (1963). ==Formal definition== More formally, the star height of a regular expression ''E'' over a finite alphabet ''A'' is inductively defined as follows: * $\backslash scriptstyle\; h\backslash left(\backslash emptyset\backslash right)\backslash ,=\backslash ,0$, $\backslash scriptstyle\; h\backslash left(\backslash varepsilon\backslash right)\backslash ,=\backslash ,0$, and $\backslash scriptstyle\; h\backslash left(a\backslash right)\backslash ,=\backslash ,0$ for all alphabet symbols ''a'' in ''A''. * $\backslash scriptstyle\; h\backslash left(E\; F\backslash right)\backslash ,=\backslash ,\; h\backslash left(E\backslash ,\; \backslash mid\backslash ,\; F\backslash right)\backslash ,=\backslash ,\backslash max\; \backslash left(\backslash ,\; h(E),\; h(F)\backslash ,\backslash right)$ * $\backslash scriptstyle\; h\backslash left(E^$ *\right)\,=\,h(E)+1. Here, $\backslash scriptstyle\; \backslash emptyset$ is the special regular expression denoting the empty set and ε the special one denoting the empty word; ''E'' and ''F'' are arbitrary regular expressions. The star height ''h''(''L'') of a regular language ''L'' is defined as the minimum star height among all regular expressions representing ''L''. The intuition is here that if the language ''L'' has large star height, then it is in some sense inherently complex, since it cannot be described by means of an "easy" regular expression, of low star height. 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「Star height」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.