All reports by Author Kaave Hosseini:

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TR18-169
| 18th September 2018
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Kaave Hosseini, Shachar Lovett, Grigory Yaroslavtsev#### Optimality of Linear Sketching under Modular Updates

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TR18-142
| 17th August 2018
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Kaave Hosseini, Shachar Lovett#### A bilinear Bogolyubov-Ruzsa lemma with poly-logarithmic bounds

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TR18-076
| 22nd April 2018
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Abhishek Bhrushundi, Kaave Hosseini, Shachar Lovett, Sankeerth Rao#### Torus polynomials: an algebraic approach to ACC lower bounds

Revisions: 1

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TR18-015
| 25th January 2018
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Eshan Chattopadhyay, Pooya Hatami, Kaave Hosseini, Shachar Lovett#### Pseudorandom Generators from Polarizing Random Walks

Revisions: 1
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Comments: 1

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TR16-044
| 21st March 2016
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Kaave Hosseini, Shachar Lovett#### Structure of protocols for XOR functions

Revisions: 1

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TR15-179
| 10th November 2015
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Divesh Aggarwal, Kaave Hosseini, Shachar Lovett#### Affine-malleable Extractors, Spectrum Doubling, and Application to Privacy Amplification

Kaave Hosseini, Shachar Lovett, Grigory Yaroslavtsev

We study the relation between streaming algorithms and linear sketching algorithms, in the context of binary updates. We show that for inputs in $n$ dimensions,

the existence of efficient streaming algorithms which can process $\Omega(n^2)$ updates implies efficient linear sketching algorithms with comparable cost.

This improves upon the previous work ...
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Kaave Hosseini, Shachar Lovett

The Bogolyubov-Ruzsa lemma, in particular the quantitative bounds obtained by Sanders, plays a central role

in obtaining effective bounds for the inverse $U^3$ theorem for the Gowers norms. Recently, Gowers and Mili\'cevi\'c

applied a bilinear Bogolyubov-Ruzsa lemma as part of a proof of the inverse $U^4$ theorem

with effective bounds.

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Abhishek Bhrushundi, Kaave Hosseini, Shachar Lovett, Sankeerth Rao

We propose an algebraic approach to proving circuit lower bounds for ACC0 by defining and studying the notion of torus polynomials. We show how currently known polynomial-based approximation results for AC0 and ACC0 can be reformulated in this framework, implying that ACC0 can be approximated by low-degree torus polynomials. Furthermore, ... more >>>

Eshan Chattopadhyay, Pooya Hatami, Kaave Hosseini, Shachar Lovett

We propose a new framework for constructing pseudorandom generators for $n$-variate Boolean functions. It is based on two new notions. First, we introduce fractional pseudorandom generators, which are pseudorandom distributions taking values in $[-1,1]^n$. Next, we use a fractional pseudorandom generator as steps of a random walk in $[-1,1]^n$ that ... more >>>

Kaave Hosseini, Shachar Lovett

Let $f:\{0,1\}^n \to \{0,1\}$ be a boolean function. Its associated XOR function is the two-party function $f_\oplus(x,y) = f(x \oplus y)$.

We show that, up to polynomial factors, the deterministic communication complexity of $f_{\oplus}$ is equal to the parity decision tree complexity of $f$.

This relies on a novel technique ...
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Divesh Aggarwal, Kaave Hosseini, Shachar Lovett

The study of seeded randomness extractors is a major line of research in theoretical computer science. The goal is to construct deterministic algorithms which can take a ``weak" random source $X$ with min-entropy $k$ and a uniformly random seed $Y$ of length $d$, and outputs a string of length close ... more >>>