All reports by Author Hamed Hatami:

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TR22-079
| 25th May 2022
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Hamed Hatami, Pooya Hatami, William Pires, Ran Tao, Rosie Zhao#### Lower Bound Methods for Sign-rank and their Limitations

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TR22-041
| 23rd March 2022
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TsunMing Cheung, Hamed Hatami, Rosie Zhao, Itai Zilberstein#### Boolean functions with small approximate spectral norm

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TR21-123
| 25th August 2021
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Ben Davis, Hamed Hatami, William Pires, Ran Tao, Hamza Usmani#### On public-coin zero-error randomized communication complexity

Revisions: 2

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TR21-066
| 5th May 2021
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Lianna Hambardzumyan, Hamed Hatami, Pooya Hatami#### Dimension-free Bounds and Structural Results in Communication Complexity

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TR19-067
| 6th May 2019
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Hamed Hatami, Kaave Hosseini, Shachar Lovett#### Sign rank vs Discrepancy

Revisions: 1

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TR19-029
| 20th February 2019
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Yuval Filmus, Lianna Hambardzumyan, Hamed Hatami, Pooya Hatami, David Zuckerman#### Biasing Boolean Functions and Collective Coin-Flipping Protocols over Arbitrary Product Distributions

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TR16-190
| 21st November 2016
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Yuval Dagan, Yuval Filmus, Hamed Hatami, Yaqiao Li#### Trading information complexity for error

Hamed Hatami, Pooya Hatami, William Pires, Ran Tao, Rosie Zhao

The sign-rank of a matrix $A$ with $\pm 1$ entries is the smallest rank of a real matrix with the same sign pattern as $A$. To the best of our knowledge, there are only three known methods for proving lower bounds on the sign-rank of explicit matrices: (i) Sign-rank is ... more >>>

TsunMing Cheung, Hamed Hatami, Rosie Zhao, Itai Zilberstein

The sum of the absolute values of the Fourier coefficients of a function $f:\mathbb{F}_2^n \to \mathbb{R}$ is called the spectral norm of $f$. Green and Sanders' quantitative version of Cohen's idempotent theorem states that if the spectral norm of $f:\mathbb{F}_2^n \to \{0,1\}$ is at most $M$, then the support of ... more >>>

Ben Davis, Hamed Hatami, William Pires, Ran Tao, Hamza Usmani

We prove that for every Boolean function, the public-coin zero-error randomized communication complexity and the deterministic communication complexity are polynomially equivalent.

more >>>Lianna Hambardzumyan, Hamed Hatami, Pooya Hatami

The purpose of this article is to initiate a systematic study of dimension-free relations between basic communication and query complexity measures and various matrix norms. In other words, our goal is to obtain inequalities that bound a parameter solely as a function of another parameter. This is in contrast to ... more >>>

Hamed Hatami, Kaave Hosseini, Shachar Lovett

Sign-rank and discrepancy are two central notions in communication complexity. The seminal work of Babai, Frankl, and Simon from 1986 initiated an active line of research that investigates the gap between these two notions.

In this article, we establish the strongest possible separation by constructing a Boolean matrix whose sign-rank ...
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Yuval Filmus, Lianna Hambardzumyan, Hamed Hatami, Pooya Hatami, David Zuckerman

The seminal result of Kahn, Kalai and Linial shows that a coalition of $O(\frac{n}{\log n})$ players can bias the outcome of *any* Boolean function $\{0,1\}^n \to \{0,1\}$ with respect to the uniform measure. We extend their result to arbitrary product measures on $\{0,1\}^n$, by combining their argument with a completely ... more >>>

Yuval Dagan, Yuval Filmus, Hamed Hatami, Yaqiao Li

We consider the standard two-party communication model. The central problem studied in this article is how much one can save in information complexity by allowing an error of $\epsilon$.

For arbitrary functions, we obtain lower bounds and upper bounds indicating a gain that is of order $\Omega(h(\epsilon))$ and $O(h(\sqrt{\epsilon}))$. ...
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