A seminal result of Nisan and Szegedy (STOC, 1992) shows that for any total Boolean function, the degree of the real polynomial that computes the function, and the minimal degree of a real polynomial that point-wise approximates the function, are at most polynomially separated. Extending this result from degree to ... more >>>

We exhibit an $n$-bit communication problem with a constant-cost randomized protocol but which requires $n^{\Omega(1)}$ deterministic (or even non-deterministic) queries to an Equality oracle. Therefore, even constant-cost randomized protocols cannot be efficiently "derandomized" using Equality oracles. This improves on several recent results and answers a question from the survey of ... more >>>

It is a well-known fact that the permanent polynomial is complete for the complexity class VNP, and it is largely suspected that the determinant does not share this property, despite its similar expression.
We study the question of why the VNP-completeness proof of the permanent fails for the determinant.
We ... more >>>