We introduce a new hierarchy over monotone set functions, that we refer to as $MPH$ (Maximum over Positive Hypergraphs).
Levels of the hierarchy correspond to the degree of complementarity in a given function.
The highest level of the hierarchy, $MPH$-$m$ (where $m$ is the total number of items) captures all ... more >>>

Non-malleable codes were introduced by Dziembowski, Pietrzak and Wichs \cite{DPW10} as an elegant generalization of the classical notions of error detection, where the corruption of a codeword is viewed as a tampering function acting on it. Informally, a non-malleable code with respect to a family of tampering functions $\mathcal{F}$ consists ... more >>>

We study internal compression of communication protocols
to their internal entropy, which is the entropy of the transcript from the players' perspective.
We first show that errorless compression to the internal entropy
(and hence to the internal information) is impossible.
We then provide two internal compression schemes with error.
One ... more >>>