SIAM Journal on Computing

We give the first efficient algorithm to approximately count the number of solutions in the random $k$-SAT model when the density of the formula scales exponentially with $k$. The best previous counting algorithm for the permissive version of the model ...

Holant problems are a family of counting problems parameterized by sets of algebraic-complex-valued constraint functions and defined on graphs. They arise from the theory of holographic algorithms, which was originally inspired by concepts from quantum ...

This paper considers a special class of nonlocal games $(G,\psi)$, where $G$ is a two-player one-round game, and $\psi$ is a bipartite state independent of $G$. In the game $(G,\psi)$, the players are allowed to share arbitrarily many copies of $\psi$. The ...

We give a deterministic $O(\log n\cdot\log\log n)$-space algorithm for approximately solving linear systems given by Laplacians of undirected graphs, and consequently also approximating hitting times, commute times, and escape probabilities for undirected ...