Boolean function

In mathematics, a finitary boolean function is a function of the form f : B^k → B, where 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 B.

More generally, a function of the form f : X → B, where X is an arbitrary set, is a boolean-valued function. If X = M = {1, 2, 3, …}, then f is a binary sequence, that is, an infinite sequence of 0's and 1's. If X = [k] = {1, 2, 3, …, k}, then f is binary sequence of length k.

There are ${\displaystyle 2^{2^{n}}}$ such functions. These 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 S-box).

A boolean mask operation on boolean-valued functions combines values point-wise (for example, by XOR, or other boolean operators).

You all suck.

See also

• Boolean algebra topics
• Boolean ___domain
• Boolean-valued function
• Truth function
• Zeroth order logic

External links

• Boolean Planet — boolean functions in cryptography.