We study depth 3 circuits of the form $\mathrm{OR} \circ \mathrm{AND} \circ \mathrm{XOR}$, or equivalently -- DNF of parities. This model was first explicitly studied by Jukna (CPC'06) who obtained a $2^{\Omega(n)}$ lower bound for explicit functions. Several related models have gained attention in the last few years, such as ... more >>>

Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design the first nontrivial approximation algorithms in this context.

Our main result is that ... more >>>

We initiate a study of super-perfect zero-knowledge proof systems.
Loosely speaking, these are proof systems for which the interaction can be perfectly simulated in strict probabilistic polynomial-time.
In contrast, the standard definition of perfect zero-knowledge only requires that the interaction can be perfectly simulated
by a strict probabilistic polynomial-time that ... more >>>