Definition:Boolean Function

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 $$2^{2^k}$$ boolean functions on $$k\!$$ variables.