The influence lower bound via query elimination
Rahul Jain, Shengyu Zhang
TL;DR
This paper presents a simplified proof technique using query elimination to establish lower bounds on the zero-error randomized query complexity of functions, relating it to variable influence, and extends these bounds to distributional complexity.
Contribution
It introduces a simpler proof method for influence-based lower bounds and extends these bounds to two-sided error distributional query complexity.
Findings
Lower bounds on zero-error randomized query complexity based on variable influence
Extension of bounds to two-sided error distributional complexity
Potential for stronger lower bounds for specific functions
Abstract
We give a simpler proof, via query elimination, of a result due to O'Donnell, Saks, Schramm and Servedio, which shows a lower bound on the zero-error randomized 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 distributional 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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Taxonomy
TopicsComplexity and Algorithms in Graphs · Cryptography and Data Security · Machine Learning and Algorithms