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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