"Help bits" are some limited trusted information about an instance or instances of a computational problem that may reduce the computational complexity of solving that instance or instances. In this paper, we study the value of help bits in the settings of randomized and average-case complexity.

Amir, Beigel, and Gasarch ... more >>>

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 >>>