In Boolean logic, the majority function (also called the median operator) is a function from n inputs to one output. The value of the operation is false when n/2 or fewer arguments are false, and true otherwise. Alternatively, representing true values as 1 and false values as 0, we may use the formula <math>\operatorname{Majority} \left (p_1,\dots,p_n \right) = \left \lfloor \frac{1}{2} + \frac{\sum_{i=1}^n p_i - 1/2}{n} \right \rfloor.

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  • In Boolean logic, the majority function (also called the median operator) is a function from n inputs to one output. The value of the operation is false when n/2 or fewer arguments are false, and true otherwise. Alternatively, representing true values as 1 and false values as 0, we may use the formula <math>\operatorname{Majority} \left (p_1,\dots,p_n \right) = \left \lfloor \frac{1}{2} + \frac{\sum_{i=1}^n p_i - 1/2}{n} \right \rfloor. </math> The "−1/2" in the formula serves to break ties in favor of zeros when n is even; a similar formula can be used for a function that breaks ties in favor of ones. A major result in circuit complexity asserts that this function cannot be computed by AC0 circuits of subexponential size. A majority gate is a logical gate used in circuit complexity and other applications of Boolean circuits. A majority gate returns true if and only if at least 50% +1 of its inputs are true.
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  • In Boolean logic, the majority function (also called the median operator) is a function from n inputs to one output. The value of the operation is false when n/2 or fewer arguments are false, and true otherwise. Alternatively, representing true values as 1 and false values as 0, we may use the formula <math>\operatorname{Majority} \left (p_1,\dots,p_n \right) = \left \lfloor \frac{1}{2} + \frac{\sum_{i=1}^n p_i - 1/2}{n} \right \rfloor.
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  • Majority function
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