The Merge Resolution proof system (M-Res) for QBFs, proposed by Beyersdorff et al. in 2019, explicitly builds partial strategies inside refutations. The original motivation for this approach was to overcome the limitations encountered in long-distance Q-Resolution proof system (LD-Q-Res), where the syntactic side-conditions, while prohibiting all unsound resolutions, also end ... more >>>

The sign-rank of a matrix $A$ with $\pm 1$ entries is the smallest rank of a real matrix with the same sign pattern as $A$. To the best of our knowledge, there are only three known methods for proving lower bounds on the sign-rank of explicit matrices: (i) Sign-rank is ... more >>>

Multiplicity codes are a generalization of Reed-Muller codes which include derivatives as well as the values of low degree polynomials, evaluated in every point in $\mathbb{F}_p^m$.
Similarly to Reed-Muller codes, multiplicity codes have a local nature that allows for local correction and local testing.
Recently, the authors and ... more >>>