We compare two methods for proving lower bounds on standard two-party model of communication complexity, the Rank method and Fooling set method. We present bounds on the number of functions $f(x,y)$, $x,y\in\{0,1\}^n$, with rank of size $k$ and fooling set of size at least k, $k\in [1,2^n]$. Using these bounds ... more >>>

A matrix is blocky if it is a blowup of a permutation matrix. The blocky rank of a matrix M is the minimum number of blocky matrices that linearly span M. Hambardzumyan, Hatami and Hatami defined blocky rank and showed that it is connected to communication complexity and operator theory. ... more >>>

It is a long-standing open problem in algebraic complexity to prove lower bounds against multilinear algebraic branching programs (mABPs). The best lower bounds in this setting are still quadratic (Alon, Kumar and Volk (Combinatorica 2020)). At the same time, it remains a possibility that the “min-partition rank” method introduced by ... more >>>