Content deleted Content added
No edit summary |
binary sequences |
||
Line 3:
:''F''(''b''<sub>1</sub>, ''b''<sub>2</sub>, ... , ''b''<sub>n</sub>)
of a number ''n'' of '''Boolean variables''' ''b''<sub>i</sub> from the two-element [[Boolean algebra]] {0,1}, and such that ''F'' also takes values in {0,1}. A function on a general [[function ___domain]] taking values in {0,1} would be called a '''''Boolean-valued function''''', so that Boolean functions are a special case. Such a function with ___domain {1,2,3, ...} is commonly called a '''binary sequence''', i.e. an [[infinite sequence]] of 0's and 1's; by restricting to {1,2,3, ..., ''n''} a Boolean function is in a natural way coded by a sequence of length ''n''.
There are 2<sup>''n''</sup> 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]]).
| |||