In this work, we design knowledge compilation languages for quantified Boolean formulas (QBFs), with a particular focus on model counting. We introduce various languages in increasing order of their power of representation, starting from a simple tree-based structure, and extending it to DAGs for a more efficient representation. We study ... more >>>

Let $\F$ be a finite field. Given $N$ distinct points $\bm{\alpha}_1,\ldots,\bm{\alpha}_N \in \F^m$ and associated values $\beta_1,\ldots,\beta_N \in \F$, we study the problem of computing an $m$-variate polynomial $f(\vy) \in \F[\vy]$ of individual degree less than $d$, with $d^m \ge N$, that satisfies $f(\bm{\alpha}_i)=\beta_i$ for all $i\in[N]$, whenever such an ... more >>>

We initiate the study of the meta-mathematics of algebraic circuit lower bounds, aiming both to gain insight into the methods sufficient and necessary to prove algebraic circuit lower bounds, and to contribute to the study of bounded arithmetic as a logical foundation for complexity lower bounds. We demonstrate that while ... more >>>