Unate function

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 :f(x_1,x_2,ldots,x_{i-1},1,x_{i+1},ldots;x_n) >= far(x_1,x_2,ldots,x_{i-1},0,x_{i+1},ldots,x_n).,Likewise, it is negative unate in x_i if :far(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 x_i "f" is either positive or negative unate in the variable x_i 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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