The Influence Lower Bound Via Query Elimination

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.

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