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/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Dinur, Khot, Kindler, Minzer and Safra (2016) recently showed that the (imperfect completeness variant of) Khot's 2 to 2 games conjecture follows from a combinatorial hypothesis about the soundness of a certain "Grassmanian agreement tester". In this work, we show that the hypothesis of Dinur et. al. follows from a conjecture we call the "Inverse Shortcode Hypothesis" characterizing the non-expanding sets of the degree-two shortcode graph. We also show the latter conjecture is equivalent to a characterization of the non-expanding sets in the Grassman graph, as hypothesized by a follow-up paper of Dinur et. al. (2017). Following our work, Khot, Minzer and Safra (2018) proved the "Inverse Shortcode Hypothesis". Combining their proof with our result and the reduction of Dinur et. al. (2016), completes the proof of the 2 to 2 conjecture with imperfect completeness. Moreover, we believe that the shortcode graph provides a useful view of both the hypothesis and the reduction, and might be useful in extending it further.

Small-Set Expansion in Shortcode Graph and the 2-to-2 Conjecture