Unate function

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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 xi if

f(x_1,x_2,\ldots,x_{i-1},1,x_{i+1},\ldots;x_n) >= f\bar(x_1,x_2,\ldots,x_{i-1},0,x_{i+1},\ldots,x_n).\,

Likewise, it is negative unate in xi if

f\bar(x_1,x_2,\ldots,x_{i-1},0,x_{i+1},\ldots;x_n) >= f(x_1,x_2,\ldots,x_{i-1},1,x_{i+1},\ldots,x_n).\,

If for every xi f is either positive or negative unate in the variable xi then it is said to be unate. A function is binate if it is not unate.

For example the Logical disjunction function or with boolean values are used for true (1) and false (0) is positive unate.

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