Boolean function

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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

• Inquiry Live
• Logic Live

Peer nodes

• Boolean Function @ InterSciWiki
• Boolean Function @ Subject Wikis
• Boolean Function @ Wikiversity
• Boolean Function @ Wikiversity Beta

Logical operators

• Exclusive disjunction
• Logical conjunction
• Logical disjunction
• Logical equality

• Logical implication
• Logical NAND
• Logical NNOR
• Negation

Related topics

• Ampheck
• Boolean domain
• Boolean function
• Boolean-valued function
• Differential logic

• Logical graph
• Minimal negation operator
• Multigrade operator
• Parametric operator
• Peirce's law

• Propositional calculus
• Sole sufficient operator
• Truth table
• Universe of discourse
• Zeroth order logic

Relational concepts

• Continuous predicate
• Hypostatic abstraction
• Logic of relatives
• Logical matrix

• Relation
• Relation composition
• Relation construction
• Relation reduction

• Relation theory
• Relative term
• Sign relation
• Triadic relation

Information, Inquiry

• Inquiry
• Dynamics of inquiry

• Semeiotic
• Logic of information

• Descriptive science
• Normative science

• Pragmatic maxim
• Truth theory

Related articles

• Cactus Language
• Futures Of Logical Graphs
• Propositional Equation Reasoning Systems

• 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, PlanetMath
• Boolean Function, Wikinfo
• Boolean Function, Wikiversity
• Boolean Function, Wikiversity Beta
• Boolean Function, Wikipedia