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 $2^{2^k}$ such functions. These play a basic role in questions of complexity theory as well as the design of circuits and chips for digital computers.

Resources

• Logic Syllabus

Document history

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.

• Boolean Function, InterSciWiki
• Boolean Function, Wikiversity
• Boolean Function, Wikipedia