We provide a digest of the paper of Fei and Rubinfeld (arXiv 2026), which provides an alternative analysis of the Bipartite Tester of Goldreich and Ron ({\em Combinatorica}, 1999), which operates in the bounded-degree graph model.
Loosely speaking, on input an $n$-vertex graph $G$, the tester selects few vertices, ... more >>>

For a propositional proof system $\mathcal{P}$ and a polynomial-time function $G: \{0, 1\}^n \to \{0, 1\}^N$ ($N > 10n$), we say that $G$ is a *proof complexity generator* against $\mathcal{P}$ if $\mathcal{P}$ cannot efficiently prove the (suitably encoded) statement "$y\not\in\mathrm{Range}(G)$" for every $y \in \{0, 1\}^N$, and $G$ is a ... more >>>

We introduce and study a new model of decision trees that lies at the frontier of provable circuit lower bounds.

We study $\ell$-local decision trees, in which each internal node queries an $\ell$-local function of the input. We show that sufficiently strong lower bounds for $\ell$-local decision trees would imply ... more >>>