Set disjointness is one of the most fundamental problems in communication complexity. In the multi-party number-in-hand version of set disjointness, $k$ players receive private inputs $X_1,\ldots,X_k\subseteq \{1,\ldots,n\}$, and their goal is to determine whether or not $\bigcap_{i = 1}^k X_i = \emptyset$. In this paper we prove a tight lower ... more >>>

We prove that finding a Nash equilibrium of a game is hard, assuming the existence of indistinguishability obfuscation and injective one-way functions with sub-exponential hardness. We do so by showing how these cryptographic primitives give rise to a hard computational problem that lies in the complexity class PPAD, for which ... more >>>

We revisit the gate elimination method, generalize it to prove correlation bounds of boolean circuits with Parity, and also derive deterministic #SAT algorithms for small linear-size circuits. In particular, we prove that, for boolean circuits of size $3n - n^{0.51}$, the correlation with Parity is at most $2^{-n^{\Omega(1)}}$, and there ... more >>>