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Electronic Colloquium on Computational Complexity

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Reports tagged with linearity testing:
TR97-010 | 2nd April 1997
Marcos Kiwi

Testing and Weight Distributions of Dual Codes

We study the testing problem, that is, the problem of determining (maybe
probabilistically) if a function to which we have oracle access
satisfies a given property.

We propose a framework in which to formulate and carry out the analyzes
of several known tests. This framework establishes a connection between
more >>>

TR99-025 | 2nd July 1999
Yonatan Aumann, Johan Hastad, Michael O. Rabin, Madhu Sudan

Linear Consistency Testing

We extend the notion of linearity testing to the task of checking
linear-consistency of multiple functions. Informally, functions
are ``linear'' if their graphs form straight lines on the plane.
Two such functions are ``consistent'' if the lines have the same
slope. We propose a variant of a test of ... more >>>

TR08-008 | 8th February 2008
Venkatesan Guruswami, Prasad Raghavendra

Constraint Satisfaction over a Non-Boolean Domain: Approximation algorithms and Unique-Games hardness

Revisions: 1

We study the approximability of the \maxcsp problem over non-boolean domains, more specifically over $\{0,1,\ldots,q-1\}$ for some integer $q$. We obtain a approximation algorithm that achieves a ratio of $C(q) \cdot k/q^k$ for some constant $C(q)$ depending only on $q$. Further, we extend the techniques of Samorodnitsky and Trevisan to ... more >>>

TR09-020 | 2nd March 2009
Venkatesan Guruswami, Prasad Raghavendra

Hardness of Solving Sparse Overdetermined Linear Systems: A 3-Query PCP over Integers.

A classic result due to Hastad established that for every constant \eps > 0, given an overdetermined system of linear equations over a finite field \F_q where each equation depends on exactly 3 variables and at least a fraction (1-\eps) of the equations can be satisfied, it is NP-hard to ... more >>>

TR12-159 | 20th November 2012
Eli Ben-Sasson, Michael Viderman

A Combinatorial Characterization of smooth LTCs and Applications

The study of locally testable codes (LTCs) has benefited from a number of nontrivial constructions discovered in recent years. Yet we still lack a good understanding of what makes a linear error correcting code locally testable and as a result we do not know what is the rate-limit of LTCs ... more >>>

TR14-002 | 8th January 2014
Roee David, Irit Dinur, Elazar Goldenberg, Guy Kindler, Igor Shinkar

Direct Sum Testing

Revisions: 1

For a string $a \in \{0,1\}^n$ its $k$-fold direct sum encoding is a function $f_a$ that takes as input sets $S \subseteq [n]$ of
size $k$ and outputs $f_a(S) = \sum_{i \in S} a_i$.
In this paper we are interested in the Direct Sum Testing Problem,
where we are given ... more >>>

TR16-080 | 18th May 2016
Oded Goldreich

Reducing testing affine spaces to testing linearity

Revisions: 1

We consider the task of testing whether a Boolean function $f:\{0,1\}^\ell\to\{0,1\}$
is the indicator function of an $(\ell-k)$-dimensional affine space.
An optimal tester for this property was presented by Parnas, Ron, and Samorodnitsky ({\em SIDMA}, 2002), by mimicking the celebrated linearity tester (of Blum, Luby and Rubinfeld, {\em JCSS}, 1993) ... more >>>

TR16-124 | 12th August 2016
Subhash Khot

On Independent Sets, $2$-to-$2$ Games and Grassmann Graphs

Revisions: 1 , Comments: 1

We present a candidate reduction from the $3$-Lin problem to the $2$-to-$2$ Games problem and present a combinatorial hypothesis about
Grassmann graphs which, if correct, is sufficient to show the soundness of the reduction in
a certain non-standard sense. A reduction that is sound in this non-standard sense
implies that ... more >>>

TR18-067 | 9th April 2018
Alessandro Chiesa, Peter Manohar, Igor Shinkar

Testing Linearity against Non-Signaling Strategies

Revisions: 1

Non-signaling strategies are collections of distributions with certain non-local correlations. They have been studied in Physics as a strict generalization of quantum strategies to understand the power and limitations of Nature's apparent non-locality. Recently, they have received attention in Theoretical Computer Science due to connections to Complexity and Cryptography.

We ... more >>>

TR18-123 | 3rd July 2018
Alessandro Chiesa, Peter Manohar, Igor Shinkar

Probabilistic Checking against Non-Signaling Strategies from Linearity Testing

Revisions: 1

Non-signaling strategies are a generalization of quantum strategies that have been studied in physics over the past three decades. Recently, they have found applications in theoretical computer science, including to proving inapproximability results for linear programming and to constructing protocols for delegating computation. A central tool for these applications is ... more >>>

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