Boolean function

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

There are ${\displaystyle 2^{2^{k}}}$ 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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