For quantified Boolean formulas (QBF) there are two main different approaches to solving: QCDCL and expansion solving. In this paper we compare the underlying proof systems and show that expansion systems admit strictly shorter proofs than CDCL systems for formulas of bounded quantifier complexity, thus pointing towards potential advantages of ... more >>>

Let $G$ be an undirected, bounded degree graph with $n$ vertices. Fix a finite graph $H$, and suppose one must remove $\varepsilon n$ edges from $G$ to make it $H$-minor free (for some small constant $\varepsilon > 0$).
We give an $n^{1/2+o(1)}$-time randomized procedure that, with high probability, finds an ... more >>>

We show that a very simple pseudorandom generator fools intersections of $k$ linear threshold functions (LTFs) and arbitrary functions of $k$ LTFs over $n$-dimensional Gaussian space.

The two analyses of our PRG (for intersections versus arbitrary functions of LTFs) are quite different from each other and from previous analyses of ... more >>>