Communication
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# 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]

## 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.

## Arity

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

## 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.

## 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.

## 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.

## Boolean data type

In computer science, the Boolean data type is a data type, having two values (usually denoted true and false), intended to represent the truth values of logic and Boolean algebra.

## Boolean domain

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

## 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.

## Computational complexity theory

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

## Computer

A computer is a general-purpose device that can be programmed to carry out a set of arithmetic or logical operations automatically.

## Cooperative game

In game theory, a cooperative game is a game where groups of players ("coalitions") may enforce cooperative behaviour, hence the game is a competition between coalitions of players, rather than between individual players.

## Cryptography

Cryptography or cryptology; from Greek κρυπτός kryptós, "hidden, secret"; and γράφειν graphein, "writing", or -λογία -logia, "study", respectively is the practice and study of techniques for secure communication in the presence of third parties (called adversaries).

## 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.

## Evasive Boolean function

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

## Finitary

In mathematics or logic, a finitary operation is an operation that takes a finite number of input values to produce an output, like those of arithmetic.

## 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.

## Function (mathematics)

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

## 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 bold or blackboard bold 1 symbol with a subscript describing the event of inclusion.

## List of Boolean algebra topics

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

## Logic

Logic (from the λογική, logike) is the branch of philosophy concerned with the use and study of valid reasoning.

## Logical connective

In logic, a logical connective (also called a logical 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 sense of the compound sentence produced depends only on the original sentences.

## Logical equivalence

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

## Mathematics

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

## 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.

## Polynomial

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

## Propositional calculus

Propositional calculus (also called propositional logic, sentential calculus, or sentential logic) is the branch of mathematical logic concerned with the study of propositions (whether they are true or false) that are formed by other propositions with the use of logical connectives, and how their value depends on the truth value of their components.

## Propositional directed acyclic graph

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

## Propositional formula

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

## S-box

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

## 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.

## 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.

## 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.

## Truth function

In mathematical logic, a truth function is a function from a set of truth values to truth values.

## Truth table

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

## References

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