Boolean function

In mathematics, 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. The properties of boolean functions play a critical role in cryptography, particularly in the design of symmetric key algorithms (see S-box).

A boolean mask operation on boolean-valued functions combines values point-wise, for example, by XOR, or other boolean operators.

See also

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• Algebra of sets
• Boolean algebra
• Boolean domain

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• Boolean value
• Boolean-valued function
• Zeroth order logic

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External links

• Boolean Planet — boolean functions in cryptography.

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, GetWiki.

• Boolean function, Wikinfo.

• Boolean function, Wikipedia.