Eli Ben-Sasson, Prahladh Harsha, Sofya Raskhodnikova

For a boolean formula \phi on n variables, the associated property

P_\phi is the collection of n-bit strings that satisfy \phi. We prove

that there are 3CNF properties that require a linear number of queries,

even for adaptive tests. This contrasts with 2CNF properties

that are testable with O(\sqrt{n}) ...
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Elena Grigorescu, Tali Kaufman, Madhu Sudan

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

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Srikanth Srinivasan, Madhu Sudan

The well-known DeMillo-Lipton-Schwartz-Zippel lemma says that $n$-variate

polynomials of total degree at most $d$ over

grids, i.e. sets of the form $A_1 \times A_2 \times \cdots \times A_n$, form

error-correcting codes (of distance at least $2^{-d}$ provided $\min_i\{|A_i|\}\geq 2$).

In this work we explore their local

decodability and local testability. ...
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