All reports by Author Ning Xie:

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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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TR10-156
| 24th October 2010
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Victor Chen, Madhu Sudan, Ning Xie#### Property Testing via Set-Theoretic Operations

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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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TR10-116
| 21st July 2010
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Arnab Bhattacharyya, Victor Chen, Madhu Sudan, Ning Xie#### Testing linear-invariant non-linear properties: A short report

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TR09-066
| 13th August 2009
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Arnab Bhattacharyya, Ning Xie#### Lower Bounds for Testing Triangle-freeness in Boolean Functions

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TR08-088
| 13th September 2008
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Arnab Bhattacharyya, Victor Chen, Madhu Sudan, Ning Xie#### Testing Linear-Invariant Non-Linear Properties

Revisions: 1

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TR07-098
| 2nd October 2007
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Tali Kaufman, Simon Litsyn, Ning Xie#### Breaking the $\epsilon$-Soundness Bound of the Linearity Test over GF(2)

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 >>>

Victor Chen, Madhu Sudan, Ning Xie

Given two testable properties $\mathcal{P}_{1}$ and $\mathcal{P}_{2}$, under what conditions are the union, intersection or set-difference

of these two properties also testable?

We initiate a systematic study of these basic set-theoretic operations in the context of property

testing. As an application, we give a conceptually different proof that linearity is ...
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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 ...
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Arnab Bhattacharyya, Victor Chen, Madhu Sudan, Ning Xie

The rich collection of successes in property testing raises a natural question: Why are so many different properties turning out to be locally testable? Are there some broad "features" of properties that make them testable? Kaufman and Sudan (STOC 2008) proposed the study of the relationship between the invariances satisfied ... more >>>

Arnab Bhattacharyya, Ning Xie

Let $f_{1},f_{2}, f_{3}:\mathbb{F}_{2}^{n} \to \{0,1\}$ be three Boolean functions.

We say a triple $(x,y,x+y)$ is a \emph{triangle} in the function-triple $(f_{1}, f_{2}, f_{3})$ if $f_{1}(x)=f_{2}(y)=f_{3}(x+y)=1$.

$(f_{1}, f_{2}, f_{3})$ is said to be \emph{triangle-free} if there is no triangle in the triple. The distance between a function-triple

and ...
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Arnab Bhattacharyya, Victor Chen, Madhu Sudan, Ning Xie

We consider the task of testing properties of Boolean functions that

are invariant under linear transformations of the Boolean cube. Previous

work in property testing, including the linearity test and the test

for Reed-Muller codes, has mostly focused on such tasks for linear

properties. The one exception is a test ...
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Tali Kaufman, Simon Litsyn, Ning Xie

For Boolean functions that are $\epsilon$-far from the set of linear functions, we study the lower bound on the rejection probability (denoted $\textsc{rej}(\epsilon)$) of the linearity test suggested by Blum, Luby and Rubinfeld. The interest in this problem is partly due to its relation to PCP constructions and hardness of ... more >>>