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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study population protocols: networks of anonymous agents that interactunder a scheduler that picks pairs of agents uniformly at random. The _sizecounting problem_ is that of calculating the exact number $n$ of agents in thepopulation, assuming no leader (each agent starts in the same state). We givethe first protocol that solves this problem in sublinear time. The protocolconverges in $O(\log n \log \log n)$ time and uses $O(n^{60})$ states ($O(1) +60 \log n$ bits of memory per agent) with probability $1-O(\frac{\log \logn}{n})$. The time complexity is also $O(\log n \log \log n)$ in expectation.The time to converge is also $O(\log n \log \log n)$ in expectation. Crucially,unlike most published protocols with $\omega(1)$ states, our protocol is_uniform_: it uses the same transition algorithm for any population size, sodoes not need an estimate of the population size to be embedded into thealgorithm. A sub-protocol is the first uniform sublinear-time leader electionpopulation protocol, taking $O(\log n \log \log n)$ time and $O(n^{18})$states. The state complexity of both the counting and leader election protocolscan be reduced to $O(n^{30})$ and $O(n^{9})$ respectively, while increasing thetime to $O(\log^2 n)$.

Exact size counting in uniform population protocols in nearly logarithmic time