The Log-Approximate-Rank Conjecture is False

Speaker: 

Time: 

Tuesday, 27 November 2018, 14:00 to 15:00

Venue: 

  • A-201 (STCS Seminar Room)

Organisers: 

Abstract: The Log-Approximate-Rank Conjecture was a long-standing conjecture which posited that the randomised communication complexity of a function and log of the approximate rank of its communication matrix are polynomially related.

In this work, we introduce a function F that refutes this conjecture. We will discuss a drawback of rank-like measures and see a proof that F has small approximate rank, yet is hard for randomised communication (joint work with Arkadev Chattopadhyay and Nikhil Mande).