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In [[mathematics]], a '''finitary boolean function''' is a [[function (mathematics)|function]] of the form <math>f : \mathbb{B}^k \to \mathbb{B},</math> where <math>\mathbb{B} = \{ 0, 1 \}</math> is a [[boolean domain]] and where <math>k\!</math> is a nonnegative integer.  In the case where <math>k = 0,\!</math> the function is simply a constant element of <math>\mathbb{B}.</math>

A '''finitary boolean function''' is a [[function (mathematics)|function]] of the form <math>f : \mathbb{B}^k \to \mathbb{B},</math> where <math>\mathbb{B} = \{ 0, 1 \}</math> is a [[boolean domain]] and where <math>k\!</math> is a nonnegative integer.  In the case where <math>k = 0,\!</math> the function is simply a constant element of <math>\mathbb{B}.</math>

There are <math>2^{2^k}</math> such functions.  These play a basic role in questions of [[complexity theory]] as well as the design of circuits and chips for [[digital computer]]s. The properties of boolean functions play a critical role in [[cryptography]], particularly in the design of [[symmetric key algorithms]] (see [[S-box]]).

There are <math>2^{2^k}</math> such functions.  These play a basic role in questions of [[complexity theory]] as well as the design of circuits and chips for digital computers.

==See also==

==Syllabus==

 

===Logical operators===

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* [[Algebra of sets]]

* [[Exclusive disjunction]]

* [[Boolean algebra]]

* [[Logical conjunction]]

 

 

* [[Ampheck]]

* [[Boolean domain]]

* [[Boolean domain]]

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* [[Boolean value]]

* [[Logical graph]]

* [[Boolean-valued function]]

* [[Logical matrix]]

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* [[Universe of discourse]]

* [[Zeroth order logic]]

* [[Zeroth order logic]]

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==Document history==

==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.

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.

* [http://www.getwiki.net/-Boolean_Function Boolean function], [http://www.getwiki.net/ GetWiki].

 

* [http://wikinfo.org/index.php/Boolean_function Boolean function], [http://wikinfo.org/index.php/Main_Page Wikinfo].

* [http://beta.wikiversity.org/wiki/Boolean_function Boolean Function], [http://beta.wikiversity.org/ Beta Wikiversity]

* [http://planetmath.org/encyclopedia/BooleanFunction.html Boolean Function], [http://planetmath.org/ PlanetMath]

* [http://www.wikinfo.org/index.php/Boolean_function Boolean Function], [http://www.wikinfo.org/ Wikinfo]

* [http://www.textop.org/wiki/index.php?title=Boolean_function Boolean Function], [http://www.textop.org/wiki/ Textop Wiki]

* [http://en.wikipedia.org/w/index.php?title=Boolean_function&oldid=60886833 Boolean Function], [http://en.wikipedia.org/ Wikipedia]

* [http://en.wikipedia.org/wiki/Boolean_function Boolean function], [http://en.wikipedia.org/ Wikipedia].

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[[Category:Boolean algebra]]

[[Category:Combinatorics]]

[[Category:Cryptography]]

[[Category:Computer Science]]

[[Category:Discrete Mathematics]]

[[Category:Logic]]

[[Category:Logic]]

[[Category:Mathematics]]

[[Category:Mathematics]]