We resolve two open problems regarding the Sherali-Adams proof system. First, we show that Res(2), which manipulates 2-DNF formulas, is exponentially stronger than Sherali-Adams. This provides a sharp separation in power between Sherali-Adams and the bounded-depth Frege hierarchy, as Sherali-Adams polynomially simulates Resolution. Second, we prove that Sherali-Adams is not ... more >>>

OpenAI's Sep 2026 preprint introduced the first cubic lower bound on the border DC of the permanent. Their preprint generalizes the method I introduced in my June 2026 preprint (https://arxiv.org/abs/2606.15970; see also TR26-275). However, their proof only applies over $\mathbb{C}$.

In this note, I prove that the cubic lower bound ... more >>>

The plural in the title hints that there are several complexities involved here.
The most traditional one is the computational complexity of the verifier; but, in the context of Interactive Proofs of Proximity (IPPs), the query complexity of the verifier and the communication complexity of the system should ... more >>>