Difference between revisions of "Boolean function"

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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>
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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]]).
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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==
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==Syllabus==
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===Logical operators===
  
 
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* [[Algebra of sets]]
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* [[Exclusive disjunction]]
* [[Boolean algebra]]
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* [[Logical conjunction]]
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* [[Logical disjunction]]
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* [[Logical equality]]
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{{col-break}}
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* [[Logical implication]]
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* [[Logical NAND]]
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* [[Logical NNOR]]
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* [[Logical negation|Negation]]
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===Related topics===
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* [[Ampheck]]
 
* [[Boolean domain]]
 
* [[Boolean domain]]
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* [[Boolean function]]
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* [[Boolean-valued function]]
 
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* [[Boolean value]]
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* [[Logical graph]]
* [[Boolean-valued function]]
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* [[Logical matrix]]
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* [[Minimal negation operator]]
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* [[Peirce's law]]
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* [[Propositional calculus]]
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* [[Truth table]]
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* [[Universe of discourse]]
 
* [[Zeroth order logic]]
 
* [[Zeroth order logic]]
 
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==External links==
 
 
* [http://www.isi.qut.edu.au/people/fuller/ Boolean Planet] — boolean functions in cryptography.
 
  
 
==Document history==
 
==Document history==
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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].
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* [http://wikinfo.org/index.php/Boolean_function Boolean function], [http://wikinfo.org/index.php/Main_Page Wikinfo].
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* [http://mywikibiz.com/Boolean_function Boolean Function], [http://mywikibiz.com/ MyWikiBiz]
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* [http://beta.wikiversity.org/wiki/Boolean_function Boolean Function], [http://beta.wikiversity.org/ Beta Wikiversity]
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* [http://planetmath.org/encyclopedia/BooleanFunction.html Boolean Function], [http://planetmath.org/ PlanetMath]
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* [http://www.wikinfo.org/index.php/Boolean_function Boolean Function], [http://www.wikinfo.org/ Wikinfo]
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* [http://www.textop.org/wiki/index.php?title=Boolean_function Boolean Function], [http://www.textop.org/wiki/ Textop Wiki]
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* [http://en.wikipedia.org/w/index.php?title=Boolean_function&oldid=60886833 Boolean Function], [http://en.wikipedia.org/ Wikipedia]
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* [http://en.wikipedia.org/wiki/Boolean_function Boolean function], [http://en.wikipedia.org/ Wikipedia].
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<br><sharethis />
  
[[Category:Boolean algebra]]
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[[Category:Combinatorics]]
[[Category:Cryptography]]
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[[Category:Computer Science]]
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[[Category:Discrete Mathematics]]
 
[[Category:Logic]]
 
[[Category:Logic]]
 
[[Category:Mathematics]]
 
[[Category:Mathematics]]

Revision as of 01:20, 7 April 2010

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.

Syllabus

Logical operators

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Related topics

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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.

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<sharethis />