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A threshold function is a Boolean function that determines whether a value equality of its inputs exceeded a certain threshold. A device that implements such logic is known as a threshold gate.

Definition

Let Equation n Boolean inputs be Equation x 1 comma x 2 comma period period period comma x Subscript n Baseline . Equation f is a function that decides whether Equation w 1 x 1 plus w 2 x 2 plus period period period plus w Subscript n Baseline x Subscript n Baseline equals t where Equation t is a real number called the threshold and Equation w 1 comma w 2 comma period period period comma w Subscript n Baseline are real-numbered weights. A threshold function on Equation n Boolean inputs Equation x 1 comma x 2 comma period period period comma x Subscript n Baseline is then a Boolean function that decides whether Equation w 1 x 1 plus w 2 x 2 plus period period period plus w Subscript n Baseline x Subscript n Baseline greater-than-or-equal-to t

Equation f left-parenthesis x 1 comma x 2 comma period period period comma x Subscript n Baseline right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column 1 comma 2nd Column w 1 x 1 plus w 2 x 2 plus period period period plus w Subscript n Baseline x Subscript n Baseline greater-than-or-equal-to t 2nd Row 1st Column 0 comma 2nd Column otherwise EndLayout

Threshold functions

See also

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