Marcos Kiwi

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

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Yonatan Aumann, Johan HÃ¥stad, Michael O. Rabin, Madhu Sudan

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 ...
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Venkatesan Guruswami, Prasad Raghavendra

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 >>>

Venkatesan Guruswami, Prasad Raghavendra

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 >>>

Eli Ben-Sasson, Michael Viderman

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 >>>

Roee David, Irit Dinur, Elazar Goldenberg, Guy Kindler, Igor Shinkar

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 ...
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Oded Goldreich

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) ...
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Subhash Khot

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 ...
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Alessandro Chiesa, Peter Manohar, Igor Shinkar

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 >>>

Alessandro Chiesa, Peter Manohar, Igor Shinkar

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 >>>

Mohammad Jahanara, Sajin Koroth, Igor Shinkar

Amey Bhangale, Subhash Khot, Dor Minzer

In this paper we study functions on the Boolean hypercube that have the property that after applying certain random restrictions, the restricted function is correlated to a linear function with non-negligible probability. If the given function is correlated with a linear function then this property clearly holds. Furthermore, the property ... more >>>