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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 Noncommutative signal-flow graph ： ウィキペディア英語版 Noncommutative signal-flow graph In automata theory and control theory, branches of mathematics, theoretical computer science and systems engineering, a noncommutative signal-flow graph is a tool for modeling interconnected systems and state machines by mapping the edges of a directed graph to a ring or semiring. A single edge weight might represent an array of impulse responses of a complex system (see figure to the right), or a character from an alphabet picked off the input tape of a finite automaton, while the graph might represent the flow of information or state transitions. As diverse as these applications are, they share much of the same underlying theory. ==Definition== Consider ''n'' equations involving ''n''+1 variables . :$x\_i\; =\; \backslash sum\_^n\; a\_x\_j,\; \backslash ;\backslash ;\backslash ;\; 1\backslash leq\; i\; \backslash leq\; n,$ with ''a''ij elements in a ring or semiring ''R''. The free variable ''x''0 corresponds to a source vertex ''v''0, thus having no defining equation. Each equation corresponds to a fragment of a directed graph ''G''=(''V'',''E'') as show in the figure. The edge weights define a function ''f'' from ''E'' to ''R''. Finally fix an output vertex ''vm''. A signal-flow graph is the collection of this data ''S'' = (''G''=(''V'',''E''), ''v0'',''vm'' $\backslash in$ ''V'', ''f'' : ''E'' → ''R''). The equations may not have a solution, but when they do, :$x\_m\; =\; T\; x\_0,$ with ''T'' an element of ''R'' called the gain. 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「Noncommutative signal-flow graph」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.