Weizmann Logo
ECCC
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



REPORTS > AUTHORS > SUHAIL SHERIF:
All reports by Author Suhail Sherif:

TR18-176 | 26th October 2018
Arkadev Chattopadhyay, Nikhil Mande, Suhail Sherif

The Log-Approximate-Rank Conjecture is False

We construct a simple and total XOR function $F$ on $2n$ variables that has only $O(\sqrt{n})$ spectral norm, $O(n^2)$ approximate rank and $n^{O(\log n)}$ approximate nonnegative rank. We show it has polynomially large randomized bounded-error communication complexity of $\Omega(\sqrt{n})$. This yields the first exponential gap between the logarithm of the ... more >>>




ISSN 1433-8092 | Imprint