We give the first super-polynomial separation in the power of bounded-depth boolean formulas vs. circuits. Specifically, we consider the problem Distance $k(n)$ Connectivity, which asks whether two specified nodes in a graph of size $n$ are connected by a path of length at most $k(n)$. This problem is solvable (by ... more >>>

In this paper we study the fractional block sensitivityof Boolean functions. Recently, Tal (ITCS, 2013) and
Gilmer, Saks, and Srinivasan (CCC, 2013) independently introduced this complexity measure, denoted by $fbs(f)$, and showed
that it is equal (up to a constant factor) to the randomized certificate complexity, denoted by $RC(f)$, which ... more >>>

We prove improved inapproximability results for hypergraph coloring using the low-degree polynomial code (aka, the “short code” of Barak et. al. [FOCS 2012]) and the techniques proposed by Dinur and Guruswami [FOCS 2013] to incorporate this code for inapproximability results.

In particular, we prove quasi-NP-hardness of the following problems on ... more >>>