Boolean Function

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This page belongs to resource collections on Logic and Inquiry.

A finitary boolean function is a function of the form <math>f : \mathbb{B}^k \to \mathbb{B},</math> where <math>\mathbb{B} = \{ 0, 1 \}</math> is a boolean domain and where <math>k\!</math> is a nonnegative integer. In the case where <math>k = 0,\!</math> the function is simply a constant element of <math>\mathbb{B}.</math>

There are <math>2^{2^k}</math> such functions. These play a basic role in questions of complexity theory as well as the design of circuits and chips for digital computers.

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