The canonical problem that gives an exponential separation between deterministic and randomized communication complexity in the classical two-party communication model is `Equality'. In this work, we show that even allowing access to an `Equality' oracle, deterministic protocols remain exponentially weaker than randomized ones. More precisely, we exhibit a total function ... more >>>

Nisan and Szegedy conjectured that block sensitivity is at most polynomial in sensitivity for any Boolean function. There is a huge gap between the best known upper bound on block sensitivity in terms of sensitivity - which is exponential, and the best known separating examples - which give only a ... more >>>

Chattopadhyay, Mande and Sherif (ECCC 2018) recently exhibited a total
Boolean function, the sink function, that has polynomial approximate rank and
polynomial randomized communication complexity. This gives an exponential
separation between randomized communication complexity and logarithm of the
approximate rank, refuting the log-approximate-rank conjecture. We show that ... more >>>