Abstract:Let f : {0, 1} n → {0, 1} be a boolean function, and let f∧(x, y) = f (x ∧ y) denote the AND-function of f , where x ∧ y denotes bit-wise AND. We study the deterministic communication complexity of f∧ and show that, up to a log n factor, it is bounded by a polynomial in the logarithm of the real rank of the communication matrix of f∧. This comes within a log n factor of establishing the log-rank conjecture for AND-functions with no assumptions on f . Our result stands in contrast with previous results on speci… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.