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In mathematics, a symmetric Boolean function is a Boolean function whose value does not depend on the permutation of its input bits, i.e., it depends only on the number of ones in the input.〔Ingo Wegener, "The Complexity of Symmetric Boolean Functions", in: ''Computation Theory and Logic'', ''Lecture Notes in Computer Science'', vol. 270, 1987, pp. 433-442〕 The definition implies that instead of the truth table, traditionally used to represent Boolean functions, one may use a more compact representation for an ''n''-variable symmetric Boolean function: the (''n'' + 1)-vector, whose ''i''-th entry (''i'' = 0, ..., ''n'') is the value of the function on an input vector with ''i'' ones. ==Special cases== A number of special cases are recognized.〔 *Threshold functions: their value is 1 on input vectors with ''k'' or more ones for a fixed ''k'' *Exact-value functions: their value is 1 on input vectors with ''k'' ones for a fixed ''k'' * Counting functions : their value is 1 on input vectors with the number of ones congruent to ''k'' mod ''m'' for fixed ''k'', ''m'' *Parity functions: their value is 1 if the input vector has odd number of ones. 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「Symmetric Boolean function」の詳細全文を読む スポンサード リンク
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