Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a (finitary) Boolean function is a function of the form ¿ : Bk ¿ B, where B = {0, 1} is a Boolean domain and k is a nonnegative integer called the arity of the function. In the case where k = 0, the "function" is essentially a constant element of B. Every k-ary Bool ...Täielik kirjeldus
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a (finitary) Boolean function is a function of the form ¿ : Bk ¿ B, where B = {0, 1} is a Boolean domain and k is a nonnegative integer called the arity of the function. In the case where k = 0, the "function" is essentially a constant element of B. Every k-ary Boolean formula 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. 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).