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>
  
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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 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.
  
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==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]]
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* [[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]]
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* [[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==
 
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* [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.
  
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* [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 />
  
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[[Category:Boolean algebra]]
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[[Category:Combinatorics]]
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[[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

Template:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-end

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.

Template:Col-breakTemplate:Col-breakTemplate:Col-end
<sharethis />
Retrieved from "https://mywikibiz.com/index.php?title=Boolean_function&oldid=115630"