|
A '''boolean mask operation''' on boolean-valued functions combines values point-wise (for example, by [[Exclusive or|XOR]], or other [[boolean operator]]s).
You all suck.
==Algebraic Normal Form==
A boolean function can be written uniquely as a sum ([[Exclusive or|XOR]]) of products ([[Logical_conjunction|AND]]). This is known as the [[Algebraic Normal Form]] (ANF).
{| cellpadding="4"
|-
|<math>f(x_1, x_2, \ldots , x_n) = \!</math>
|<math>a_0 + \!</math>
|-
|
|<math>a_1x_1 + a_2x_2 + \ldots + a_nx_n + \!</math>
|-
|
|<math>a_{1,2}x_1x_2 + a_{n-1,n}x_{n-1}x_n + \!</math>
|-
|
|<math>\ldots + \!</math>
|-
|
|<math>a_{1,2,\ldots,n}x_1x_2\ldots x_n \!</math>
|}
The values of the sequence <math>a_0,a_1,\ldots,a_{1,2,\ldots,n}</math> can therefore also uniquely represent a boolean function. The algebraic degree of a boolean function is defined as the highest number of <math>x_i</math> that appear in a product term. Thus <math>f(x_1,x_2,x_3) = x_1 + x_3</math> has degree 1 (linear), whereas <math>f(x_1,x_2,x_3) = x_1 + x_1x_2x_3</math> has degree 3 (cubic).
==See also==
| 