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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 <math>f(x_1,x_2,\ldots,x_n)</math> is said to be '''positive unate''' in <math>x_i</math> | |||
if for all <math>x_j</math>, <math>j\neq i</math> | |||
:<math>f(x_1,x_2,\ldots,x_{i-1},1,x_{i+1},\ldots,x_n) \ge f(x_1,x_2,\ldots,x_{i-1},0,x_{i+1},\ldots,x_n).\,</math> | |||
Likewise, it is '''negative unate''' in <math>x_i</math> if | |||
:<math>f(x_1,x_2,\ldots,x_{i-1},0,x_{i+1},\ldots,x_n) \ge f(x_1,x_2,\ldots,x_{i-1},1,x_{i+1},\ldots,x_n).\,</math> | |||
If for every <math>x_i</math> ''f'' is either positive or negative unate in the variable <math>x_i</math> then it is said to be '''unate''' (note that some <math>x_i</math> may be positive and some negative to satisfy the definition of unate). A function is '''binate''' if it is not unate (i.e., is neither positive nor negative in at least one of its variables). | |||
For example the [[Logical disjunction]] function ''or'' with boolean values are 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) | |||
[[Category:Syntax (logic)]] | |||
{{Compu-lang-stub}} | |||
Latest revision as of 01:48, 17 March 2013
A unate function is a type of boolean function which has monotonic properties. They have been studied extensively in switching theory.
A function is said to be positive unate in if for all ,
Likewise, it is negative unate in if
If for every f is either positive or negative unate in the variable then it is said to be unate (note that some may be positive and some negative to satisfy the definition of unate). A function is binate if it is not unate (i.e., is neither positive nor negative in at least one of its variables).
For example the Logical disjunction function or with boolean values are 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)
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