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In [[mathematics]], a '''finitary boolean function''' is a [[function (mathematics)|function]] of the form <math>f : \mathbb{B}^k \to \mathbb{B},</math> where <math>\mathbb{B} = \{ 0, 1 \}</math> is a [[boolean domain]] and where <math>k\!</math> is a nonnegative integer.  In the case where <math>k = 0,\!</math> the function is simply a constant element of <math>\mathbb{B}.</math>

In [[mathematics]], a '''finitary boolean function''' is a [[function (mathematics)|function]] of the form <math>f : \mathbb{B}^k \to \mathbb{B},</math> where <math>\mathbb{B} = \{ 0, 1 \}</math> is a [[boolean domain]] and where <math>k\!</math> is a nonnegative integer.  In the case where <math>k = 0,\!</math> the function is simply a constant element of <math>\mathbb{B}.</math>

There are <math>2^{2^k}</math> such functions.  These play a basic role in questions of [[complexity theory]] as well as the design of circuits and chips for [[digital computer]]s. The properties of boolean functions play a critical role in [[cryptography]], particularly in the design of [[symmetric key algorithm]]s (see [[S-box]]).

There are <math>2^{2^k}</math> such functions.  These play a basic role in questions of [[complexity theory]] as well as the design of circuits and chips for [[digital computer]]s. The properties of boolean functions play a critical role in [[cryptography]], particularly in the design of [[symmetric key algorithms]] (see [[S-box]]).

==See also==

==See also==