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Electronic Colloquium on Computational Complexity

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All reports by Author Elena Grigorescu:

TR15-030 | 6th March 2015
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

$\mathrm{AC}^{0} \circ \mathrm{MOD}_2$ 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 >>>

TR13-090 | 18th June 2013
Elena Grigorescu, Karl Wimmer, Ning Xie

Tight Lower Bounds for Testing Linear Isomorphism

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 >>>

TR11-165 | 8th December 2011
Elena Grigorescu, Chris Peikert

List Decoding Barnes-Wall Lattices

Revisions: 2

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 >>>

TR11-079 | 9th May 2011
Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, Madhu Sudan

On Sums of Locally Testable Affine Invariant Properties

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 ... more >>>

TR11-075 | 6th May 2011
Arnab Bhattacharyya, Elena Grigorescu, Prasad Raghavendra, Asaf Shapira

Testing Odd-Cycle-Freeness in Boolean Functions

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 >>>

TR10-161 | 25th October 2010
Arnab Bhattacharyya, Elena Grigorescu, Asaf Shapira

A Unified Framework for Testing Linear-Invariant Properties

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 >>>

TR10-136 | 26th August 2010
Arnab Bhattacharyya, Elena Grigorescu, Jakob Nordström, Ning Xie

Separations of Matroid Freeness Properties

Revisions: 1

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 >>>

TR09-079 | 21st September 2009
Victor Chen, Elena Grigorescu, Ronald de Wolf

Efficient and Error-Correcting Data Structures for Membership and Polynomial Evaluation

Revisions: 1

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 ... more >>>

TR09-046 | 9th May 2009
Arnab Bhattacharyya, Elena Grigorescu, Kyomin Jung, Sofya Raskhodnikova, David P. Woodruff

Transitive-Closure Spanners of the Hypercube and the Hypergrid

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 >>>

TR09-043 | 18th May 2009
Elena Grigorescu, Tali Kaufman, Madhu Sudan

Succinct Representation of Codes with Applications to Testing

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
more >>>

TR08-033 | 21st March 2008
Elena Grigorescu, Tali Kaufman, Madhu Sudan

2-Transitivity is Insufficient for Local Testability

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
more >>>

TR08-020 | 7th March 2008
Irit Dinur, Elena Grigorescu, Swastik Kopparty, Madhu Sudan

Decodability of Group Homomorphisms beyond the Johnson Bound

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 >>>

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