Dana Moshkovitz

In this work we analyze a direct product test in which each of two provers receives a subset of size n of a ground set U,

and the two subsets intersect in about (1-\delta)n elements.

We show that if each of the provers provides labels to the n ...
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Irit Dinur, Inbal Livni Navon

Given a function $f:[N]^k\rightarrow[M]^k$, the Z-test is a three query test for checking if a function $f$ is a direct product, namely if there are functions $g_1,\dots g_k:[N]\to[M]$ such that $f(x_1,\ldots,x_k)=(g_1(x_1),\dots g_k(x_k))$ for every input $x\in [N]^k$.

This test was introduced by Impagliazzo et. al. (SICOMP 2012), who ...
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Irit Dinur, Yuval Filmus, Prahladh Harsha

Agreement tests are a generalization of low degree tests that capture a local-to-global phenomenon, which forms the combinatorial backbone of most PCP constructions. In an agreement test, a function is given by an ensemble of local restrictions. The agreement test checks that the restrictions agree when they overlap, and the ... more >>>

Irit Dinur, Konstantin Golubev

A function f:[n_1] x ... x [n_d]-->F is a direct sum if it is of the form f(a_1,...,a_d) = f_1(a_1) + ... + f_d (a_d) (mod 2) for some d functions f_i:[n_i]-->F_i for all i=1,...,d. We present a 4-query test which distinguishes between direct sums and functions that are ...
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Mohammad Jahanara, Sajin Koroth, 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 >>>