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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 Functional decomposition ： ウィキペディア英語版 Functional decomposition Functional decomposition refers broadly to the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed (i.e., recomposed) from those parts by function composition. In general, this process of decomposition is undertaken either for the purpose of gaining insight into the identity of the constituent components (which may reflect individual physical processes of interest, for example), or for the purpose of obtaining a compressed representation of the global function, a task which is feasible only when the constituent processes possess a certain level of ''modularity'' (i.e., independence or non-interaction). Interactions between the components are critical to the function of the collection. All interactions may not be observable, but possibly deduced through repetitive perception, synthesis, validation and verification of composite behavior. == Basic mathematical definition == For a multivariate function $y\; =\; f(x\_1,x\_2,\backslash dots,x\_n)$, functional decomposition generally refers to a process of identifying a set of functions $\backslash$ such that :$f(x\_1,x\_2,\backslash dots,x\_n)\; =\; \backslash phi(g\_1(x\_1,x\_2,\backslash dots,x\_n),\; g\_2(x\_1,x\_2,\backslash dots,x\_n),\; \backslash dots\; g\_m(x\_1,x\_2,\backslash dots,x\_n))$ where $\backslash phi$ is some other function. Thus, we would say that the function $f$ is decomposed into functions $\backslash$. This process is intrinsically hierarchical in the sense that we can (and often do) seek to further decompose the functions $g\_i$ into a collection of constituent functions $\backslash$such that :$g\_i(x\_1,x\_2,\backslash dots,x\_n)\; =\; \backslash gamma(h\_1(x\_1,x\_2,\backslash dots,x\_n),\; h\_2(x\_1,x\_2,\backslash dots,x\_n),\; \backslash dots\; h\_p(x\_1,x\_2,\backslash dots,x\_n))$ where $\backslash gamma$ is some other function. Decompositions of this kind are interesting and important for a wide variety of reasons. In general, functional decompositions are worthwhile when there is a certain "sparseness" in the dependency structure; that is, when constituent functions are found to depend on approximately disjoint sets of variables. Thus, for example, if we can obtain a decomposition of $x\_1\; =\; f(x\_2,x\_3,\backslash dots,x\_6)$ into a hierarchical composition of functions $\backslash$ such that $x\_1\; =\; g\_1(x\_2)$, $x\_2\; =\; g\_2(x\_3,x\_4,x\_5)$, $x\_5\; =\; g\_3(x\_6)$, as shown in the figure at right, this would probably be considered a highly valuable decomposition. 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「Functional decomposition」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.