One of the central questions in space complexity is whether nondeterministic logspace computations (NL) can be simulated in unambiguous logspace (UL). A stronger notion, reach unambiguity (RUL $\subseteq$ UL $\cap$ coUL), requires every configuration reachable from the start to have exactly one computation path (Buntrock et.al. 91). While directed graph ... more >>>

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 >>>