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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