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Boolean function

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

There are $$2^{2^k}$$ 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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Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.