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Volume 7 (2011) Article 10 pp. 147-153 [Note]
The Influence Lower Bound Via Query Elimination
Received: March 4, 2011
Published: July 19, 2011
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Keywords: randomized query complexity, influence of variables
ACM Classification: F.1.3
AMS Classification: 68Q17

Abstract: [Plain Text Version]

We give a simple proof, via query elimination, of a result due to O'Donnell, Saks, Schramm, and Servedio, which shows a lower bound on the zero-error expected query complexity of a function $f$ in terms of the maximum influence of any variable of $f$. Our lower bound also applies to the two-sided error expected query complexity of $f$, and it allows an immediate extension which can be used to prove stronger lower bounds for some functions.