Decision Trees and Influence: an Inductive Proof of the OSSS Inequality

: We give a simple proof of the OSSS inequality (O'Donnell, Saks, Schramm, Servedio, FOCS 2005). The inequality states that for any decision tree T calculating a Boolean function f : {0,1}n {-1,1}, we have Var[f] i i(T)Infi(f), where i(T) is the probability that the input variable xi is read by T and Infi(f) is the influence of the ith variable on f.

• Type: Journal
• Year: 2010
• Where: TOC
• Authors: Homin K. Lee
• Keywords: Boolean Function, Input Variable Xi, Management, OSSS Inequality, TOC 2010