A binary decision diagram and truth table of a ternary Boolean function
Logical connectives
AND
, , , ,
equivalent
, ,
implies
, ,
NAND
, , ,
nonequivalent
, ,
NOR
, ,
NOT
, , ,
OR
, , ,
XNOR
XOR
,
converse
, ,
Related concepts
Propositional calculus
Predicate logic
Boolean algebra
Truth table
Truth function
Boolean function
Functional completeness
Applications
Digital logic
Programming languages
Mathematical logic
Philosophy of logic
Category
v
t
e
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}).[1][2] Alternative names are switching function, used especially in older computer science literature,[3][4] and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory.[5]
A Boolean function takes the form , where is known as the Boolean domain and is a non-negative integer called the arity of the function. In the case where , the function is a constant element of . A Boolean function with multiple outputs, with is a vectorial or vector-valued Boolean function (an S-box in symmetric cryptography).[6]
There are different Boolean functions with arguments; equal to the number of different truth tables with entries.
Every -ary Boolean function can be expressed as a propositional formula in variables , and two propositional formulas are logically equivalent if and only if they express the same Boolean function.
^"Boolean function - Encyclopedia of Mathematics". encyclopediaofmath.org. Retrieved 2021-05-03.
^Weisstein, Eric W. "Boolean Function". mathworld.wolfram.com. Retrieved 2021-05-03.
^Davies, D. W. (December 1957). "Switching Functions of Three Variables". IRE Transactions on Electronic Computers. EC-6 (4): 265–275. doi:10.1109/TEC.1957.5222038. ISSN 0367-9950.
^McCluskey, Edward J. (2003-01-01), "Switching theory", Encyclopedia of Computer Science, GBR: John Wiley and Sons Ltd., pp. 1727–1731, ISBN 978-0-470-86412-8, retrieved 2021-05-03
^Cite error: The named reference :2 was invoked but never defined (see the help page).
In mathematics, a Booleanfunction is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1})...
Look up Boolean, Booleans, or boolean in Wiktionary, the free dictionary. Any kind of logic, function, expression, or theory based on the work of George...
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the...
optimal provided that the heuristic they use is monotonic. In Boolean algebra, a monotonic function is one such that for all ai and bi in {0,1}, if a1 ≤ b1...
called a linearly separable Booleanfunction, or threshold Booleanfunction. The sequence of numbers of threshold Booleanfunctions on n inputs is OEIS A000609...
operators, and Boolean-valued functions. Boolean expressions correspond to propositional formulas in logic and are a special case of Boolean circuits. Most...
Each gate corresponds to some Booleanfunction that takes a fixed number of bits as input and outputs a single bit. Boolean circuits provide a model for...
In Boolean logic, the majority function (also called the median operator) is the Booleanfunction that evaluates to false when half or more arguments are...
Boolean operation or Boolean operator may refer to: Booleanfunction, a function whose arguments and result assume values from a two-element set Boolean...
In mathematics, a symmetric Booleanfunction is a Booleanfunction whose value does not depend on the order of its input bits, i.e., it depends only on...
In mathematics and computer science, a balanced booleanfunction is a booleanfunction whose output yields as many 0s as 1s over its input set. This means...
Analysis of Booleanfunctions Balanced booleanfunction Bent functionBoolean algebras canonically defined BooleanfunctionBoolean matrix Boolean-valued function...
above function is considered affine in linear algebra (i.e. not linear). A Booleanfunction is linear if one of the following holds for the function's truth...
In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY...
The NAND Booleanfunction has the property of functional completeness. This means that any Boolean expression can be re-expressed by an equivalent expression...
mathematical table used in logic—specifically in connection with Boolean algebra, Booleanfunctions, and propositional calculus—which sets out the functional...
connectives or Boolean operators is one that can be used to express all possible truth tables by combining members of the set into a Boolean expression....
of Boolean algebra discussing changes of Boolean variables and Booleanfunctions. Boolean differential calculus concepts are analogous to those of classical...
A logic gate is a device that performs a Booleanfunction, a logical operation performed on one or more binary inputs that produces a single binary output...
and theoretical computer science, analysis of Booleanfunctions is the study of real-valued functions on { 0 , 1 } n {\displaystyle \{0,1\}^{n}} or {...
features contain every Booleanfunction on k{\displaystyle k} Boolean variables, with each one exactly once. Viewing these Booleanfunctions as polynomials in...
Booleanfunction is said to be linearly separable provided these two sets of points are linearly separable. The number of distinct Booleanfunctions is...
In computer science, the Boolean (sometimes shortened to Bool) is a data type that has one of two possible values (usually denoted true and false) which...
branching program is a data structure that is used to represent a Booleanfunction. On a more abstract level, BDDs can be considered as a compressed representation...
A Boolean network consists of a discrete set of boolean variables each of which has a Booleanfunction (possibly different for each variable) assigned...
In Boolean algebra, a parity function is a Booleanfunction whose value is one if and only if the input vector has an odd number of ones. The parity function...
Global Information
Category
