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Unate function : ウィキペディア英語版
Unate function

A unate function is a type of boolean function which has monotonic properties.
They have been studied extensively in switching theory.
A function f(x_1,x_2,\ldots,x_n) is said to be positive unate in x_i
if for all possible values of x_j, j\neq i
:f(x_1,x_2,\ldots,x_,1,x_,\ldots,x_n) \ge f(x_1,x_2,\ldots,x_,0,x_,\ldots,x_n).\,
Likewise, it is negative unate in x_i if
:f(x_1,x_2,\ldots,x_,0,x_,\ldots,x_n) \ge f(x_1,x_2,\ldots,x_,1,x_,\ldots,x_n).\,
If for every x_i ''f'' is either positive or negative unate in the variable x_i then it is said to be unate (note that some x_i may be positive unate and some negative unate to satisfy the definition of unate function). A function is binate if it is not unate (i.e., is neither positive unate nor negative unate in at least one of its variables).
For example the Logical disjunction function ''or'' with boolean values used for true (1) and false (0) is positive unate.
NB: positive unateness can also be considered as passing the same slope (no change in the input) and negative unate is passing the opposite slope....
non unate is dependence on more than one input (of same or different slopes)


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「Unate function」の詳細全文を読む



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