Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in any circuit computing them, a complexity measure that interpolates between monotone functions and ... more >>>

We present a list of parameterized problems together with a complexity classification of whether they allow a fixed-parameter tractable reduction to SAT or not. These parameterized problems are based on problems whose complexity lies at the second level of the Polynomial Hierarchy or higher. The list will be updated as ... more >>>

We propose a candidate Lasserre integrality gap construction for the Unique Games problem.
Our construction is based on a suggestion in [KM STOC'11] wherein the authors study the complexity of approximately solving a system of linear equations over reals and suggest it as an avenue towards a (positive) resolution ... more >>>