We continue the study of welfare maximization in unit-demand (matching) markets, in a distributed information model
where agent's valuations are unknown to the central planner, and therefore communication is required to determine an
efficient allocation. Dobzinski, Nisan and Oren (STOC'14) showed that if the market size is $n$, ... more >>>

We exhibit families of 4-CNF formulas over n variables that have sums-of-squares (SOS) proofs of unsatisfiability of degree (a.k.a. rank) d but require SOS proofs of size n^{Omega(d)} for values of d = d(n) from constant all the way up to n^{delta} for some universal constant delta. This shows that ... more >>>

We consider the \emph{black-box} polynomial identity testing problem for a sub-class of
depth-4 circuits. Such circuits compute polynomials of the following type:
$
C(x) = \sum_{i=1}^k \prod_{j=1}^{d_i} Q_{i,j},
$
where $k$ is the fan-in of the top $\Sigma$ gate and $r$ is the maximum degree of the ... more >>>