We pioneer a new technique that allows us to prove a multitude of previously open simulations in QBF proof complexity. In particular, we show that extended QBF Frege p-simulates clausal proof systems such as IR-Calculus, IRM-Calculus, Long-Distance Q-Resolution, and Merge Resolution.
These results are obtained by taking a technique ... more >>>

We construct an explicit $\varepsilon$-hitting set generator (HSG) for regular ordered branching programs of length $n$ and $\textit{unbounded width}$ with a single accept state that has seed length
\[O(\log(n)(\log\log(n)+\log(1/\varepsilon))).\]
Previously, the best known seed length for regular branching programs of width $w$ with a single accept state was ... more >>>

In this note, we show the mixing of three-term progressions $(x, xg, xg^2)$ in every finite quasirandom group, fully answering a question of Gowers. More precisely, we show that for any $D$-quasirandom group $G$ and any three sets $A_1, A_2, A_3 \subset G$, we have
\[ \left|\Pr_{x,y\sim G}\left[ x \in ... more >>>