Category:Monotone function
Contents
Definition
For two vectors [math]x,y \in \{-1,1\}^n[/math], define a partial order relation by
[math]x \leq y \iff x_i \leq y_i ~~ \forall i = 1\ldots n.[/math]
A monotone Boolean function is a Boolean function [math]f:\{-1,1\}^n \to \{-1,1\}[/math] which is monotone in its input:
[math]x \leq y \Rightarrow f(x) \leq f(y) [/math].
Properties
- TODO: Add properties about stability and noise sensitivity. See Mossel and O'Donnell.
Examples
References
Pages in category "Monotone function"
The following 11 pages are in this category, out of 11 total.
