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 Plus

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

Zendy Tools

Zendy Open

The Sensitivity Conjecture and the Log-rank Conjecture are among the mostimportant and challenging problems in concrete complexity. Incidentally, theSensitivity Conjecture is known to hold for monotone functions, and so is theLog-rank Conjecture for $f(x \wedge y)$ and $f(x\oplus y)$ with monotonefunctions $f$, where $\wedge$ and $\oplus$ are bit-wise AND and XOR,respectively. In this paper, we extend these results to functions $f$ whichalternate values for a relatively small number of times on any monotone pathfrom $0^n$ to $1^n$. These deepen our understandings of the two conjectures,and contribute to the recent line of research on functions with smallalternating numbers.

Sensitivity Conjecture and Log-rank Conjecture for functions with small alternating numbers