Improved Algorithm for Tolerant Junta Testing

TL;DR

This paper presents an improved algorithm for tolerant junta testing of boolean functions, reducing query complexity and narrowing the parameter gap compared to previous methods.

Contribution

The authors introduce a more efficient algorithm that improves query complexity and parameter gap in tolerant junta testing over prior work.

Findings

Reduced query complexity compared to previous algorithms.

Narrowed the parameter gap in tolerant junta testing.

Removed the exponential term in query complexity from prior work.

Abstract

In this paper, we consider the problem of tolerant junta testing for boolean function. Compared with the prior work by Blais et al., we provide improved results in terms of both the parameter gap and query complexity. Compared with the prior work by De et al., our work did not close the parameter gap, but we removed the $2^k$ term of the query complexity.