New direct-product testers and 2-query PCPs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Local list-decoding and testing of random linear codes from high error
Proceedings of the forty-second ACM symposium on Theory of computing
The structure of winning strategies in parallel repetition games
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Some recent results on local testing of sparse linear codes
Property testing
Some recent results on local testing of sparse linear codes
Property testing
Parallel repetition of entangled games
Proceedings of the forty-third annual ACM symposium on Theory of computing
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Given a function f : X -{0,1}, its `ell’ wise direct productis the function F = f`ell : X^ell - {0,1}^ell defined by:F(x_1,...,x_ell)= (f(x_1),..,f(x_ell)).: We are interestedin the local testability of the direct product encoding(mapping f- f^ell). Namely, given an arbitrary functionF : X^ell-{0,1}^ell, we wish to determine how close itis to f`ell for some f : X-{0,1}, by making two randomqueries into F. In this work we analyze the case of lowacceptance probability of the test. We show that even ifthe test passes with small probability, epsilon 0, already Fmust have a non-trivial structure and in particular mustagree with some f^ell on nearly epsilon of the domain. Moreover,we give a structural characterization of all functions Fon which the test passes with probability epsilon.Our results can be viewed as a combinatorial analogof the low error ‘low degree test’, that is used in PCPconstructions.