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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 Pseudo-Boolean function ： ウィキペディア英語版 Pseudo-Boolean function In mathematics and optimization, a pseudo-Boolean function is a function of the form :$f:\backslash mathbf^n\; \backslash rightarrow\; \backslash mathbb$, where B =  is a ''Boolean domain'' and ''n'' is a nonnegative integer called the arity of the function. Any pseudo-Boolean function can be written uniquely as a multi-linear polynomial: :$f(\backslash boldsymbol)\; =\; a\; +\; \backslash sum\_i\; a\_ix\_i\; +\; \backslash sum\_a\_x\_ix\_j\; +\; \backslash sum\_a\_x\_ix\_jx\_k\; +\; \backslash ldots$ An important class of pseudo-Boolean functions are the submodular functions, because polynomial-time algorithms exists for minimizing them. The degree of the pseudo-Boolean function is simply the degree of the polynomial. In many settings (e.g., in Fourier analysis of pseudo-Boolean functions), a pseudo-Boolean function is viewed as a function $f$ that maps $\backslash ^n$ to $\backslash mathbb$. Again in this case we can uniquely write $f$ as a multi-linear polynomial: $f(x)=\; \backslash sum\_\backslash hat(I)\backslash prod\_x\_i,$ where $\backslash hat(I)$ are Fourier coefficients of $f$ and $()=\backslash$. For a nice and simple introduction to Fourier analysis of pseudo-Boolean functions, see.〔O'Donnell, 2008〕 ==Optimization== Minimizing (or, equivalently, maximizing) a pseudo-Boolean function is NP-hard. This can easily be seen by formulating, for example, the maximum cut problem as maximizing a pseudo-Boolean function. 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「Pseudo-Boolean function」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.