Boolean function
In mathematics and logic, a (finitary) Boolean function (or switching function) is a function of the form ƒ : Bk → B, where B = {0, 1} is a Boolean domain and k is a non-negative integer called the arity of the function.
Contents
Description
In the case where k = 0, the "function" is essentially a constant element of B.
Every k-ary Boolean function can be expressed as a propositional formula in k variables x1, …, xk, and two propositional formulas are logically equivalent if and only if they express the same Boolean function. There are 22k k-ary functions for every k.
Applications
A Boolean function describes how to determine a Boolean value output based on some logical calculation from Boolean inputs.
Such functions play a basic role in questions of complexity theory as well as the design of circuits and chips for digital computers.
The properties of Boolean functions play a critical role in cryptography, particularly in the design of symmetric key algorithms (see substitution box).
Representation
Boolean functions are often represented by sentences in propositional logic, and sometimes as multivariate polynomials over GF(2).
More efficient representations includee:
Cooperative game theory
In cooperative game theory, monotone Boolean functions are called simple games (voting games)
This notion is applied to solve problems in social choice theory.
Not to be confused with
See also
- Complexity theory
- Cryptography
- Digital computer
- Function (mathematics)
- Logic
- Mathematical logic
- Mathematics
- Propositional logic
External links
- Boolean function @ Wikipedia
