Category:Balanced function
Definition
A Boolean function [math]f:\{-1,1\}^n \to \{-1,1\}[/math] is balanced if it obtains the value 1 on exactly half of its inputs. This can be written as:
[math]\sum_{x\in\{-1,1\}^n} f(x) = 0[/math].
This also has a probabilistic view: if [math]X[/math] is a uniformly random vector in [math]\{-1,1\}^n[/math], then [math]\mathbb{E}f(X) = 0[/math].
A function which is not balanced is biased.
Properties
- TODO
Examples of balanced functions
References
Pages in category "Balanced function"
The following 17 pages are in this category, out of 17 total.
