Mildly Exponential Lower Bounds on Tolerant Testers for Monotonicity, Unateness, and Juntas.
X. Chen and
A. De and
Y. Li and
S. Nadimpalli and
R. Servedio.
15th Innovations in Theoretical Computer Science Conference (ITCS), 2024.
Abstract:
We give the first super-polynomial (in fact, mildly exponential) lower bounds for tolerant testing (equivalently, distance estimation) of monotonicity, unateness, and juntas with a \emph{constant} separation between the ``yes'' and ``no'' cases. Specifically, we give
A $2^{\Omega(n^{1/4}/\sqrt{\eps})}$-query lower bound for non-adaptive, two-sided tolerant monotonicity testers and unateness testers when the ``gap'' parameter $\eps_2-\eps_1$ is equal to $\eps$, for any $\eps \geq 1/\sqrt{n}$;
A $2^{\Omega(k^{1/2})}$-query lower bound for non-adaptive, two-sided tolerant junta testers when the gap parameter is an absolute constant.
In the constant-gap regime no non-trivial prior lower bound was known for monotonicity, the best prior lower bound known for unateness was $\tilde{\Omega}(n^{3/2})$ queries, and the best prior lower bound known for juntas was $\poly(k)$ queries.
pdf of full version on arxiv
Back to
main papers page