We give very short and simple proofs of the following statements: Given a $2$-colorable $4$-uniform hypergraph on $n$ vertices,

(1) It is NP-hard to color it with $\log^\delta n$ colors for some $\delta>0$.
(2) It is $quasi$-NP-hard to color it with $O\left({\log^{1-o(1)} n}\right)$ colors.

In terms of ... more >>>

[ This paper is a (self contained) chapter in a new book on computational complexity theory, called Mathematics and Computation, available at https://www.math.ias.edu/avi/book ].

I attempt to give here a panoramic view of the Theory of Computation, that demonstrates its place as a revolutionary, disruptive science, and as a central, ... more >>>

Let $\pi$ be an efficient two-party protocol that given security parameter $\kappa$, both parties output single bits $X_\kappa$ and $Y_\kappa$, respectively. We are interested in how $(X_\kappa,Y_\kappa)$ ``appears'' to an efficient adversary that only views the transcript $T_\kappa$. We make the following contributions:

\begin{itemize}
\item We develop new tools to ... more >>>