Property testers are fast randomized algorithms whose task is to distinguish between inputs satisfying some predetermined property ${\cal P}$ and those that are far from satisfying it. Since these algorithms operate by inspecting a small randomly selected portion of the input, the most natural property one would like to be ... more >>>

An $(n,r,s)$-design, or $(n,r,s)$-partial Steiner system, is an $r$-uniform hypergraph over $n$ vertices with pairwise hyperedge intersections of size $0$, we extract from $(N,K,n,k)$-adversarial sources of locality $0$, where $K\geq N^\delta$ and $k\geq\text{polylog }n$. The previous best result (Chattopadhyay et al., STOC 2020) required $K\geq N^{1/2+o(1)}$. As a result, we ... more >>>

We show that is hard to find regular or even ordered (also known as Davis-Putnam) Resolution proofs, extending the breakthrough result for general Resolution from Atserias and Müller to these restricted forms. Namely, regular and ordered Resolution are automatable if and only if P = NP. Specifically, for a CNF ... more >>>