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Boolean function

Index Boolean function

In mathematics and logic, a (finitary) Boolean function (or switching function) is a function of the form ƒ: Bk → B, where B. [1]

36 relations: Algebra of sets, Arity, Balanced boolean function, Binary decision diagram, Boolean algebra, Boolean differential calculus, Boolean domain, Boolean-valued function, Computational complexity theory, Computer, Cooperative game theory, Cryptography, Decision tree model, Evasive Boolean function, Finitary, Finite field, Function (mathematics), Indicator function, List of Boolean algebra topics, Logic, Logical connective, Logical equivalence, Mathematics, Negation normal form, Polynomial, Propositional calculus, Propositional directed acyclic graph, Propositional formula, Pseudo-Boolean function, Read-once function, S-box, Social choice theory, Symmetric Boolean function, Symmetric-key algorithm, Truth function, Truth table.

Algebra of sets

The algebra of sets defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion.

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Arity

In logic, mathematics, and computer science, the arity of a function or operation is the number of arguments or operands that the function takes.

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Balanced boolean function

In mathematics and computer science, a balanced boolean function is a boolean function whose output yields as many 0s as 1s over its input set.

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Binary decision diagram

In computer science, a binary decision diagram (BDD) or branching program is a data structure that is used to represent a Boolean function.

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Boolean algebra

In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.

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Boolean differential calculus

Boolean differential calculus (BDC) (German: Boolescher Differentialkalkül (BDK)) is a subject field of Boolean algebra discussing changes of Boolean variables and Boolean functions.

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Boolean domain

In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true.

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Boolean-valued function

A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f: X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B.

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Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

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Computer

A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.

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Cooperative game theory

In game theory, a cooperative game (or coalitional game) is a game with competition between groups of players ("coalitions") due to the possibility of external enforcement of cooperative behavior (e.g. through contract law).

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Cryptography

Cryptography or cryptology (from κρυπτός|translit.

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Decision tree model

In computational complexity and communication complexity theories the decision tree model is the model of computation or communication in which an algorithm or communication process is considered to be basically a decision tree, i.e., a sequence of branching operations based on comparisons of some quantities, the comparisons being assigned the unit computational cost.

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Evasive Boolean function

In mathematics, an evasive Boolean function ƒ (of n variables) is a Boolean function for which every decision tree algorithm has running time of exactly n.

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Finitary

In mathematics or logic, a finitary operation is an operation of finite arity, that is an operation that takes a finite number of input values.

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Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Indicator function

In mathematics, an indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A. It is usually denoted by a symbol 1 or I, sometimes in boldface or blackboard boldface, with a subscript specifying the subset.

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List of Boolean algebra topics

This is a list of topics around Boolean algebra and propositional logic.

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Logic

Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.

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Logical connective

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the value of the compound sentence produced depends only on that of the original sentences and on the meaning of the connective.

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Logical equivalence

In logic, statements p and q are logically equivalent if they have the same logical content.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Negation normal form

In mathematical logic, a formula is in negation normal form if the negation operator (\lnot) is only applied to variables and the only other allowed Boolean operators are conjunction (\land) and disjunction (\lor). Negation normal form is not a canonical form: for example, a \land (b\lor \lnot c) and (a \land b) \lor (a \land \lnot c) are equivalent, and are both in negation normal form.

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Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

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Propositional calculus

Propositional calculus is a branch of logic.

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Propositional directed acyclic graph

A propositional directed acyclic graph (PDAG) is a data structure that is used to represent a Boolean function.

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Propositional formula

In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value.

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Pseudo-Boolean function

In mathematics and optimization, a pseudo-Boolean function is a function of the form where B.

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Read-once function

In mathematics, a read-once function is a special type of Boolean function that can be described by a Boolean expression in which each variable appears only once.

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S-box

In cryptography, an S-box (substitution-box) is a basic component of symmetric key algorithms which performs substitution.

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Social choice theory

Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a collective decision or social welfare in some sense.

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Symmetric Boolean function

In mathematics, a symmetric Boolean function is a Boolean function whose value does not depend on the permutation of its input bits, i.e., it depends only on the number of ones in the input.

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Symmetric-key algorithm

Symmetric-key algorithms are algorithms for cryptography that use the same cryptographic keys for both encryption of plaintext and decryption of ciphertext.

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Truth function

In logic, a truth function is a function that accepts truth values as input and produces a truth value as output, i.e., the input and output are all truth values.

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Truth table

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables (Enderton, 2001).

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Redirects here:

A boolean function, Boolean Function, Boolean functions, Boolean valued function, Finitary boolean function, Switching Function, Switching function.

References

[1] https://en.wikipedia.org/wiki/Boolean_function

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