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Electronic Colloquium on Computational Complexity

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

TR23-138 | 12th September 2023
Lianna Hambardzumyan, Toniann Pitassi, Suhail Sherif, Morgan Shirley, Adi Shraibman

An improved protocol for ExactlyN with more than 3 players

The ExactlyN problem in the number-on-forehead (NOF) communication setting asks $k$ players, each of whom can see every input but their own, if the $k$ input numbers add up to $N$. Introduced by Chandra, Furst and Lipton in 1983, ExactlyN is important for its role in understanding the strength of ... more >>>


TR22-172 | 2nd December 2022
Arkadev Chattopadhyay, Nikhil Mande, Swagato Sanyal, Suhail Sherif

Lifting to Parity Decision Trees Via Stifling

We show that the deterministic decision tree complexity of a (partial) function or relation $f$ lifts to the deterministic parity decision tree (PDT) size complexity of the composed function/relation $f \circ g$ as long as the gadget $g$ satisfies a property that we call stifling. We observe that several simple ... more >>>


TR20-132 | 7th September 2020
Arkadev Chattopadhyay, Ankit Garg, Suhail Sherif

Towards Stronger Counterexamples to the Log-Approximate-Rank Conjecture

We give improved separations for the query complexity analogue of the log-approximate-rank conjecture i.e. we show that there are a plethora of total Boolean functions on $n$ input bits, each of which has approximate Fourier sparsity at most $O(n^3)$ and randomized parity decision tree complexity $\Theta(n)$. This improves upon the ... more >>>


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 >>>




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