Michele Zito

We prove that, with high probability, the space complexity of refuting

a random unsatisfiable boolean formula in $k$-CNF on $n$

variables and $m = \Delta n$ clauses is

$O(n \cdot \Delta^{-\frac{1}{k-2}})$.

Esther Ezra, Shachar Lovett

Motivated by the Beck-Fiala conjecture, we study discrepancy bounds for random sparse set systems. Concretely, these are set systems $(X,\Sigma)$, where each element $x \in X$ lies in $t$ randomly selected sets of $\Sigma$, where $t$ is an integer parameter. We provide new bounds in two regimes of parameters. We ... more >>>