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 present an intimate connection among the following fields:  (a) distributed local algorithms: coming from the area of computer science,  (b) finitary factors of iid processes: coming from the area of analysis ofrandomized processes,  (c) descriptive combinatorics: coming from the area of combinatorics andmeasure theory.  In particular, we study locally checkable labellings in grid graphs from allthree perspectives. Most of our results are for the perspective (b) where weprove time hierarchy theorems akin to those known in the field (a) [Chang,Pettie FOCS 2017]. This approach that borrows techniques from the fields (a)and (c) implies a number of results about possible complexities of finitaryfactor solutions. Among others, it answers three open questions of [Holroyd etal. Annals of Prob. 2017] or the more general question of [Brandt et al. PODC2017] who asked for a formal connection between the fields (a) and (b). Ingeneral, we hope that our treatment will help to view all three perspectives asa part of a common theory of locality, in which we follow the insightful paperof [Bernshteyn 2020+] .

Local Problems on Grids from the Perspective of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics