All reports by Author Elena Grigorescu:

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TR15-030
| 6th March 2015
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Mahdi Cheraghchi, Elena Grigorescu, Brendan Juba, Karl Wimmer, Ning Xie#### ${\mathrm{AC}^{0} \circ \mathrm{MOD}_2}$ lower bounds for the Boolean Inner Product

Revisions: 1

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TR13-090
| 18th June 2013
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Elena Grigorescu, Karl Wimmer, Ning Xie#### Tight Lower Bounds for Testing Linear Isomorphism

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TR11-165
| 8th December 2011
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Elena Grigorescu, Chris Peikert#### List Decoding Barnes-Wall Lattices

Revisions: 2

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TR11-079
| 9th May 2011
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Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, Madhu Sudan#### On Sums of Locally Testable Affine Invariant Properties

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TR11-075
| 6th May 2011
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Arnab Bhattacharyya, Elena Grigorescu, Prasad Raghavendra, Asaf Shapira#### Testing Odd-Cycle-Freeness in Boolean Functions

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TR10-161
| 25th October 2010
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Arnab Bhattacharyya, Elena Grigorescu, Asaf Shapira#### A Unified Framework for Testing Linear-Invariant Properties

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TR10-136
| 26th August 2010
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Arnab Bhattacharyya, Elena Grigorescu, Jakob NordstrÃ¶m, Ning Xie#### Separations of Matroid Freeness Properties

Revisions: 1

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TR09-079
| 21st September 2009
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Victor Chen, Elena Grigorescu, Ronald de Wolf#### Efficient and Error-Correcting Data Structures for Membership and Polynomial Evaluation

Revisions: 1

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TR09-046
| 9th May 2009
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Arnab Bhattacharyya, Elena Grigorescu, Kyomin Jung, Sofya Raskhodnikova, David P. Woodruff#### Transitive-Closure Spanners of the Hypercube and the Hypergrid

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TR09-043
| 18th May 2009
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Elena Grigorescu, Tali Kaufman, Madhu Sudan#### Succinct Representation of Codes with Applications to Testing

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TR08-033
| 21st March 2008
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Elena Grigorescu, Tali Kaufman, Madhu Sudan#### 2-Transitivity is Insufficient for Local Testability

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TR08-020
| 7th March 2008
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Irit Dinur, Elena Grigorescu, Swastik Kopparty, Madhu Sudan#### Decodability of Group Homomorphisms beyond the Johnson Bound

Mahdi Cheraghchi, Elena Grigorescu, Brendan Juba, Karl Wimmer, Ning Xie

$\mathrm{AC}^{0} \circ \mathrm{MOD}_2$ circuits are $\mathrm{AC}^{0}$ circuits augmented with a layer of parity gates just above the input layer. We study the $\mathrm{AC}^{0} \circ \mathrm{MOD}_2$ circuit lower bound for computing the Boolean Inner Product functions. Recent works by Servedio and Viola (ECCC TR12-144) and Akavia et al. (ITCS 2014) have ... more >>>

Elena Grigorescu, Karl Wimmer, Ning Xie

We study lower bounds for testing membership in families of linear/affine-invariant Boolean functions over the hypercube. A family of functions $P\subseteq \{\{0,1\}^n \rightarrow \{0,1\}\}$ is linear/affine invariant if for any $f\in P$, it is the case that $f\circ L\in P$ for any linear/affine transformation $L$ of the domain. Motivated by ... more >>>

Elena Grigorescu, Chris Peikert

The question of list decoding error-correcting codes over finite fields (under the Hamming metric) has been widely studied in recent years. Motivated by the similar discrete structure of linear codes and point lattices in $R^{N}$, and their many shared applications across complexity theory, cryptography, and coding theory, we initiate the ... more >>>

Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, Madhu Sudan

Affine-invariant properties are an abstract class of properties that generalize some

central algebraic ones, such as linearity and low-degree-ness, that have been

studied extensively in the context of property testing. Affine invariant properties

consider functions mapping a big field $\mathbb{F}_{q^n}$ to the subfield $\mathbb{F}_q$ and include all

properties that form ...
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Arnab Bhattacharyya, Elena Grigorescu, Prasad Raghavendra, Asaf Shapira

Call a function $f: \mathbb{F}_2^n \to \{0,1\}$ odd-cycle-free if there are no $x_1, \dots, x_k \in \mathbb{F}_2^n$ with $k$ an odd integer such that $f(x_1) = \cdots = f(x_k) = 1$ and $x_1 + \cdots + x_k = 0$. We show that one can distinguish odd-cycle-free functions from those $\epsilon$-far ... more >>>

Arnab Bhattacharyya, Elena Grigorescu, Asaf Shapira

The study of the interplay between the testability of properties of Boolean functions and the invariances acting on their domain which preserve the property was initiated by Kaufman and Sudan (STOC 2008). Invariance with respect to F_2-linear transformations is arguably the most common symmetry exhibited by natural properties of Boolean ... more >>>

Arnab Bhattacharyya, Elena Grigorescu, Jakob NordstrÃ¶m, Ning Xie

Properties of Boolean functions on the hypercube that are invariant

with respect to linear transformations of the domain are among some of

the most well-studied properties in the context of property testing.

In this paper, we study a particular natural class of linear-invariant

properties, called matroid freeness properties. These properties ...
more >>>

Victor Chen, Elena Grigorescu, Ronald de Wolf

We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability and for the remaining queries, the

decoder with high probability either answers correctly or declares ``don't know.'' Furthermore, if there is no ...
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Arnab Bhattacharyya, Elena Grigorescu, Kyomin Jung, Sofya Raskhodnikova, David P. Woodruff

Given a directed graph $G = (V,E)$ and an integer $k \geq 1$, a $k$-transitive-closure-spanner ($k$-TC-spanner) of $G$ is a directed graph $H = (V, E_H)$ that has (1) the same transitive-closure as $G$ and (2) diameter at most $k$. Transitive-closure spanners were introduced in \cite{tc-spanners-soda} as a common abstraction ... more >>>

Elena Grigorescu, Tali Kaufman, Madhu Sudan

Motivated by questions in property testing, we search for linear

error-correcting codes that have the ``single local orbit'' property:

i.e., they are specified by a single local

constraint and its translations under the symmetry group of the

code. We show that the dual of every ``sparse'' binary code

whose coordinates

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Elena Grigorescu, Tali Kaufman, Madhu Sudan

A basic goal in Property Testing is to identify a

minimal set of features that make a property testable.

For the case when the property to be tested is membership

in a binary linear error-correcting code, Alon et al.~\cite{AKKLR}

had conjectured that the presence of a {\em single} low weight

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Irit Dinur, Elena Grigorescu, Swastik Kopparty, Madhu Sudan

Given a pair of finite groups $G$ and $H$, the set of homomorphisms from $G$ to $H$ form an error-correcting code where codewords differ in at least $1/2$ the coordinates. We show that for every pair of {\em abelian} groups $G$ and $H$, the resulting code is (locally) list-decodable from ... more >>>