翻訳と辞書 Words near each other ・ Dyce railway station ・ Dyce stones ・ Dyce, Manitoba railway station ・ Dycer ・ Dycer baronets ・ Dychawica, Lublin Voivodeship ・ Dyche ・ Dycheiidae ・ Dychko ・ Dychlino ・ Dychtwald ・ Dychów ・ Dyck ・ Dyck Arboretum of the Plains ・ Dyck graph ・ Dyck language ・ Dyckerhoff & Widmann ・ Dyckesville, Wisconsin ・ Dyckhoff ・ Dyckia ・ Dyckia 'June' ・ Dyckia 'Lad Cutak' ・ Dyckia 'Naked Lady' ・ Dyckia 'Vista' ・ Dyckia agudensis ・ Dyckia argentea ・ Dyckia bracteata ・ Dyckia brevifolia ・ Dyckia cabrerae ・ Dyckia choristaminea Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Dyck language ： ウィキペディア英語版 Dyck language In the theory of formal languages of computer science, mathematics, and linguistics, the Dyck language is the language consisting of balanced strings of square brackets (and ). It is important in the parsing of expressions that must have a correctly nested sequence of brackets, such as arithmetic or algebraic expressions. It is named after the mathematician Walther von Dyck. ==Formal definition== Let $\backslash Sigma\; =\; \backslash$ be the alphabet consisting of the symbols (and ) and let $\backslash Sigma^$ denote its Kleene closure. For any element $u\; \backslash in\; \backslash Sigma^$ with length $|\; u\; |$ we define partial functions $insert\; :\; \backslash Sigma^\; \backslash times\; \backslash mathbb\; \backslash cup\; \backslash \; \backslash rightarrow\; \backslash Sigma^$ and $delete\; :\; \backslash Sigma^\; \backslash times\; \backslash mathbb\; \backslash rightarrow\; \backslash Sigma^$ by :$insert(u,\; j)$ is $u$ with "$[]$" inserted into the $j$th position :$delete(u,\; j)$ is $u$ with "$[]$" deleted from the $j$th position with the understanding that $insert(u,\; j)$ is undefined for $j\; >\; |u|$ and $delete(u,\; j)$ is undefined if $j\; >\; |u|\; -\; 2$. We define an equivalence relation $R$ on $\backslash Sigma^$ as follows: for elements $a,\; b\; \backslash in\; \backslash Sigma^$ we have $(a,\; b)\; \backslash in\; R$ if and only if there exists a finite sequence of applications of the $insert$ and $delete$ functions starting with $a$ and ending with $b$, where the empty sequence is allowed. That the empty sequence is allowed accounts for the reflexivity of $R$. Symmetry follows from the observation that any finite sequence of applications of $insert$ to a string can be undone with a finite sequence of applications of $delete$. Transitivity is clear from the definition. The equivalence relation partitions the language $\backslash Sigma^$ into equivalence classes. If we take $\backslash epsilon$ to denote the empty string, then the language corresponding to the equivalence class $\backslash operatorname(\backslash epsilon)$ is called the Dyck language. 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「Dyck language」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.