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2009
ACM

New direct-product testers and 2-query PCPs

14 years 7 months ago
New direct-product testers and 2-query PCPs
The "direct product code" of a function f gives its values on all k-tuples (f(x1), . . . , f(xk)). This basic construct underlies "hardness amplification" in cryptography, circuit complexity and PCPs. Goldreich and Safra [12] pioneered its local testing and its PCP application. A recent result by Dinur and Goldenberg [5] enabled for the first time testing proximity to this important code in the "list-decoding" regime. In particular, they give a 2-query test which works for polynomially small success probability 1/k , and show that no such test works below success probability 1/k. Our main result is a 3-query test which works for exponentially small success probability exp(-k ). Our techniques (based on recent simplified decoding algorithms for the same code [15]) also allow us to considerably simplify the analysis of the 2-query test of [5]. We then show how to derandomize their test, achieving a code of polynomial rate, independent of k, and success prob...
Russell Impagliazzo, Valentine Kabanets, Avi Wigde
Added 23 Nov 2009
Updated 23 Nov 2009
Type Conference
Year 2009
Where STOC
Authors Russell Impagliazzo, Valentine Kabanets, Avi Wigderson
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