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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 Matrix grammar ： ウィキペディア英語版 Matrix grammar A matrix grammar is a formal grammar in which instead of single productions, productions are grouped together into finite sequences. A production cannot be applied separately, it must be applied in sequence. In the application of such a sequence of productions, the rewriting is done in accordance to the each production in sequence, the first one, second one etc. till the last production has been used for rewriting. The sequences are referred to as matrices. Matrix grammar is an extension of context-free grammar, and one instance of a Controlled grammar. == Formal definition == A ''matrix grammar'' is an ordered quadruple :$G\; =\; (V\_N,\; V\_T,\; X\_0,\; M).$ where * $V\_N$ is a finite set of non-terminals * $V\_T$ is a finite set of terminals * $X\_0$ is a special element of $V\_N$, viz. the starting symbol * $M$ is a finite set of non-empty sequences whose elements are ordered pairs :$(P,\; Q),\; \backslash quad\; P\; \backslash in\; W(V)\; V\_N\; W(V),\; \backslash quad\; Q\; \backslash in\; W(V),\; \backslash quad\; V\; =\; V\_N\; \backslash cup\; V\_T.$ The pairs are called productions, written as $P\; \backslash to\; Q$. The sequences are called matrices and can be written as :$m\; =\; (\backslash to\; Q\_1,\; \backslash ldots,\; P\_r\; \backslash to\; Q\_r).$ Let $F$ be the set of all productions appearing in the matrices $m$ of a matrix grammar $G$. Then the matrix grammar $G$ is of type-$i,\; i\; =\; 0,\; 1,\; 2,\; 3$, ''length-increasing'', ''linear'', ''$\backslash lambda$-free'', ''context-free'' or ''context-sensitive'' if and only if the grammar $G\_1\; =\; (V\_N,\; V\_T,\; X\_0,\; F)$ has the following property. For a matrix grammar $G$, a binary relation $\backslash Rightarrow\_G$ is defined; also represented as $\backslash Rightarrow$. For any $P,\; Q\; \backslash in\; W(V)$, $P\; \backslash Rightarrow\; Q$ holds if and only if there exists an integer $r\; \backslash ge\; 1$ such that the words :$\backslash alpha\_1,,\; \backslash ldots,\; \backslash alpha\_,\; \backslash quad\; P\_1,\; \backslash ldots,\; P\_r,\; \backslash quad\; R\_1,\; \backslash ldots,\; R\_r,\; \backslash quad,\; R^1,\; \backslash ldots,\; R^r$ over V exist and * $\backslash alpha\_i\; =\; P$ and $\backslash alpha\_\; =\; Q$ * $m$ is one of the matrices of $G$ * $\backslash alpha\_i\; =\; R\_i\; P\_i\; R^i$ and $\backslash alpha\_\; =\; R\_i\; Q\_i\; R^i.$ If the above conditions are satisfied, it is also said that $P\; \backslash Rightarrow\; Q$ holds with $(m,\; R\_1)$ as the ''specifications''. Let $\backslash Rightarrow^$ be the reflexive transitive closure of the relation $\backslash Rightarrow$. Then, the language generated by the matrix grammar $G$ is given by :$L(G)\; =\; \backslash .$ 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「Matrix grammar」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.