Difference between revisions of "Boolean function"
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− | + | <font size="3">☞</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. | |
− | + | 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 computers. | |
− | == | + | ==Syllabus== |
− | + | ===Focal nodes=== | |
− | + | * [[Inquiry Live]] | |
− | + | * [[Logic Live]] | |
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− | + | ===Peer nodes=== | |
− | == | + | * [http://intersci.ss.uci.edu/wiki/index.php/Boolean_function Boolean Function @ InterSciWiki] |
+ | * [http://mywikibiz.com/Boolean_function Boolean Function @ MyWikiBiz] | ||
+ | * [http://ref.subwiki.org/wiki/Boolean_function Boolean Function @ Subject Wikis] | ||
+ | * [http://en.wikiversity.org/wiki/Boolean_function Boolean Function @ Wikiversity] | ||
+ | * [http://beta.wikiversity.org/wiki/Boolean_function Boolean Function @ Wikiversity Beta] | ||
+ | |||
+ | ===Logical operators=== | ||
+ | |||
+ | {{col-begin}} | ||
+ | {{col-break}} | ||
+ | * [[Exclusive disjunction]] | ||
+ | * [[Logical conjunction]] | ||
+ | * [[Logical disjunction]] | ||
+ | * [[Logical equality]] | ||
+ | {{col-break}} | ||
+ | * [[Logical implication]] | ||
+ | * [[Logical NAND]] | ||
+ | * [[Logical NNOR]] | ||
+ | * [[Logical negation|Negation]] | ||
+ | {{col-end}} | ||
+ | |||
+ | ===Related topics=== | ||
{{col-begin}} | {{col-begin}} | ||
{{col-break}} | {{col-break}} | ||
− | * [[ | + | * [[Ampheck]] |
− | |||
* [[Boolean domain]] | * [[Boolean domain]] | ||
+ | * [[Boolean function]] | ||
+ | * [[Boolean-valued function]] | ||
+ | * [[Differential logic]] | ||
+ | {{col-break}} | ||
+ | * [[Logical graph]] | ||
+ | * [[Minimal negation operator]] | ||
+ | * [[Multigrade operator]] | ||
+ | * [[Parametric operator]] | ||
+ | * [[Peirce's law]] | ||
{{col-break}} | {{col-break}} | ||
− | * [[ | + | * [[Propositional calculus]] |
− | * [[ | + | * [[Sole sufficient operator]] |
+ | * [[Truth table]] | ||
+ | * [[Universe of discourse]] | ||
* [[Zeroth order logic]] | * [[Zeroth order logic]] | ||
{{col-end}} | {{col-end}} | ||
− | == | + | ===Relational concepts=== |
+ | |||
+ | {{col-begin}} | ||
+ | {{col-break}} | ||
+ | * [[Continuous predicate]] | ||
+ | * [[Hypostatic abstraction]] | ||
+ | * [[Logic of relatives]] | ||
+ | * [[Logical matrix]] | ||
+ | {{col-break}} | ||
+ | * [[Relation (mathematics)|Relation]] | ||
+ | * [[Relation composition]] | ||
+ | * [[Relation construction]] | ||
+ | * [[Relation reduction]] | ||
+ | {{col-break}} | ||
+ | * [[Relation theory]] | ||
+ | * [[Relative term]] | ||
+ | * [[Sign relation]] | ||
+ | * [[Triadic relation]] | ||
+ | {{col-end}} | ||
+ | |||
+ | ===Information, Inquiry=== | ||
+ | |||
+ | {{col-begin}} | ||
+ | {{col-break}} | ||
+ | * [[Inquiry]] | ||
+ | * [[Dynamics of inquiry]] | ||
+ | {{col-break}} | ||
+ | * [[Semeiotic]] | ||
+ | * [[Logic of information]] | ||
+ | {{col-break}} | ||
+ | * [[Descriptive science]] | ||
+ | * [[Normative science]] | ||
+ | {{col-break}} | ||
+ | * [[Pragmatic maxim]] | ||
+ | * [[Truth theory]] | ||
+ | {{col-end}} | ||
+ | |||
+ | ===Related articles=== | ||
− | * [http:// | + | {{col-begin}} |
+ | {{col-break}} | ||
+ | * [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language] | ||
+ | * [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs] | ||
+ | * [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems] | ||
+ | {{col-break}} | ||
+ | * [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction] | ||
+ | * [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus] | ||
+ | * [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems] | ||
+ | {{col-break}} | ||
+ | * [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems] | ||
+ | * [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems] | ||
+ | * [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry] | ||
+ | {{col-end}} | ||
==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:// | + | * [http://intersci.ss.uci.edu/wiki/index.php/Boolean_function Boolean Function], [http://intersci.ss.uci.edu/ InterSciWiki] |
− | + | * [http://mywikibiz.com/Boolean_function Boolean Function], [http://mywikibiz.com/ MyWikiBiz] | |
− | * [http://wikinfo.org/index.php/Boolean_function Boolean | + | * [http://planetmath.org/BooleanValuedFunction Boolean Function], [http://planetmath.org/ PlanetMath] |
− | + | * [http://wikinfo.org/w/index.php/Boolean_function Boolean Function], [http://wikinfo.org/w/ Wikinfo] | |
− | * [http://en.wikipedia.org/ | + | * [http://en.wikiversity.org/wiki/Boolean_function Boolean Function], [http://en.wikiversity.org/ Wikiversity] |
+ | * [http://beta.wikiversity.org/wiki/Boolean_function Boolean Function], [http://beta.wikiversity.org/ Wikiversity Beta] | ||
+ | * [http://en.wikipedia.org/w/index.php?title=Boolean_function&oldid=60886833 Boolean Function], [http://en.wikipedia.org/ Wikipedia] | ||
− | [[Category: | + | [[Category:Inquiry]] |
− | [[Category: | + | [[Category:Open Educational Resource]] |
+ | [[Category:Peer Educational Resource]] | ||
+ | [[Category:Combinatorics]] | ||
+ | [[Category:Computer Science]] | ||
+ | [[Category:Discrete Mathematics]] | ||
[[Category:Logic]] | [[Category:Logic]] | ||
[[Category:Mathematics]] | [[Category:Mathematics]] |
Latest revision as of 20:24, 5 November 2015
☞ This page belongs to resource collections on Logic and Inquiry.
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
Focal nodes
Peer nodes
- Boolean Function @ InterSciWiki
- Boolean Function @ MyWikiBiz
- Boolean Function @ Subject Wikis
- Boolean Function @ Wikiversity
- Boolean Function @ Wikiversity Beta
Logical operators
Template:Col-breakTemplate:Col-breakTemplate:Col-endRelated topics
- Propositional calculus
- Sole sufficient operator
- Truth table
- Universe of discourse
- Zeroth order logic
Relational concepts
Information, Inquiry
Related articles
- Differential Logic : Introduction
- Differential Propositional Calculus
- Differential Logic and Dynamic Systems
- Prospects for Inquiry Driven Systems
- Introduction to Inquiry Driven Systems
- Inquiry Driven Systems : Inquiry Into Inquiry
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, MyWikiBiz
- Boolean Function, PlanetMath
- Boolean Function, Wikinfo
- Boolean Function, Wikiversity
- Boolean Function, Wikiversity Beta
- Boolean Function, Wikipedia