English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

The \direct product code" of a function f gives its values on all k-tuples (f(x1);:::;f(xk)). This basic construct under- lies \hardness amplication" in cryptography, circuit com- plexity 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,rst time test- ing 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 exponen- tially small success probability exp( k ). Our techniques (based on recent simplied,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 probability 1=k . Finally we show the applicability of the new tests to PCPs. Starting with a 2-query PCP over an alphabet,and with soundness error 1 , Rao [19] (building on Raz’s (k-fold) parallel repetition theorem [20] and Holenstein’s proof [13])

New direct-product testers and 2-query PCPs