Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff

We consider two known lower bounds on randomized communication complexity: The smooth rectangle bound and the logarithm of the approximate non-negative rank. Our main result is that they are the same up to a multiplicative constant and a small additive term.

The logarithm of the nonnegative rank is known to ...
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Arkadev Chattopadhyay, Nikhil Mande, Suhail Sherif

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 >>>