Distance-Sensitive Property Testing Lower Bounds

TL;DR

This paper establishes new lower bounds on the query complexity for property testing problems, specifically for monotonicity and low Fourier degree, highlighting the dependence on the distance parameter.

Contribution

It provides the first matching lower bounds for monotonicity testing that align with recent upper bounds, advancing understanding of query complexity.

Findings

Lower bounds for monotonicity testing match recent upper bounds.

New lower bounds for testing low Fourier degree functions.

Clarifies the dependence of query complexity on the distance parameter.

Abstract

In this paper, we consider several property testing problems and ask how the query complexity depends on the distance parameter $\eps$. We achieve new lower bounds in this setting for the problems of testing whether a function is monotone and testing whether the function has low Fourier degree. For monotonicity testing, our lower bound matches the recent upper bound of Chakrabarty and Seshadhri.