An Additive Combinatorics Approach Relating Rank to Communication Complexity

For a $\{0, 1\}$-valued matrix $M$ let $\cc(M)$ denote the deterministic communication complexity of the boolean function associated with $M$. It is well-known since the work of Mehlhorn and Schmidt [STOC 1982] that $\cc(M)$ is bounded from above by $\...

The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Boolean function is polynomially related to the non-...

We formulate several questions concerning the intersections of sets of Boolean roots of low degree polynomials. Two of these questions we show to be equivalent to the Log-Rank Conjecture from communication complexity. We further exhibit a slightly ...