Several proof systems for model counting have been introduced in recent years, mainly in an attempt to model #SAT solving and to allow proof logging of solvers. We reexamine these different approaches and show that: (i) with slight adaptations, the conceptually quite different proof models of the dynamic system MICE ... more >>>

In this work, we give an optimal analysis of the plane versus plane test of Raz and Safra (STOC'97). More specifically, consider a table $T$ that assigns every plane $P$ from $\mathbb{F}_q^m$ a bivariate degree $d$ polynomial. The goal is to check if these polynomials are restrictions of a global ... more >>>

We consider the question of whether worst-case hardness of the time-bounded Kolmogorov complexity problem, $\KpolyA$---that is, determining whether a string is time-bounded Kolmogorov random ($K^t$-random) or not---suffices to imply the existence of one-way functions (OWF).
Roughly speaking, our main result shows that under a natural strengthening of standard-type derandomization ... more >>>