Let f be a product of D generic linear forms in m variables over a field of characteristic 0, and for integers k, l >= 0 let Gamma_{k,l}(f) = dim S_l * partial^k f be its shifted partial derivative measure, the complexity measure behind the known lower bounds for homogeneous ... more >>>

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 >>>