Considering the bounded-degree graph model, we show that if the degree bound is two,
then every graph property can be tested within query complexity that only depends on the proximity parameter.
Specifically, the query complexity is ${\rm poly}(1/\epsilon)$, where $\epsilon$ denotes the proximity parameter.
The key observation is that a ... more >>>

In this paper, we obtain several new results on lower bounds and derandomization for ACC^0 circuits (constant-depth circuits consisting of AND/OR/MOD_m gates for a fixed constant m, a frontier class in circuit complexity):

1. We prove that any polynomial-time Merlin-Arthur proof system with an ACC^0 verifier (denoted by ... more >>>

Rossman [In Proc. 34th Comput. Complexity Conf., 2019] introduced the notion of criticality. The criticality of a Boolean function $f : \{0, 1\}^n\to \{0, 1\}$ is the minimum $\lambda \geq 1$ such that for all positive integers $t$,
\[Pr_{\rho\sim R_p} [\text{DT}_{\text{depth}}(f|_\rho) \geq t] \leq (p\lambda)^t.\]
.
Håstad’s celebrated switching lemma ... more >>>