We prove that, assuming the Unique Games Conjecture (UGC), every problem in the class of ordering constraint satisfaction problems (OCSP) where each constraint has constant arity is approximation
resistant. In other words, we show that if $\rho$ is the expected fraction of constraints satisfied by a random ordering, then obtaining ... more >>>

A Boolean function $f \colon \mathbb{F}^n_2 \rightarrow \mathbb{F}_2$ is called an affine disperser for sources of dimension $d$, if $f$ is not constant on any affine subspace of $\mathbb{F}^n_2$ of dimension at least $d$. Recently Ben-Sasson and Kopparty gave an explicit construction of an affine disperser for $d=o(n)$. The main ... more >>>

In the paper, we introduce the concept of monotone rank, and using it as a powerful tool, we obtain several important and strong separation results in computational complexity.

\begin{itemize}

\item We show a super-exponential separation between monotone and non-monotone computation in the non-commutative model, and thus give the answer to ... more >>>