从分布式算法、有限因子与描述性组合数学视角看网格上的局部问题
Local Problems on Grids from the Perspective of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics
AI总结：
本研究建立了分布式局部算法、独立同分布过程有限因子与描述性组合数学三个领域的关联，通过研究网格图局部可校验标注，证明有限因子领域的时间层次定理，解答了相关开放问题，推动了统一局部性理论的构建。
摘要：
我们揭示了以下三个领域之间的紧密联系：（a）分布式局部算法：源自计算机科学领域；（b）独立同分布过程的有限因子（finitary factors of iid processes）：源自随机过程分析领域；（c）描述性组合数学（descriptive combinatorics）：源自组合数学与测度论领域。具体而言，我们从这三个视角出发，研究了网格图中的局部可校验标注问题。我们的大部分结果围绕视角（b）展开，证明了与领域（a）中已知结论[Chang, Pettie FOCS 2017]类似的时间层次定理。这种借鉴领域（a）和（c）技术的方法，推导出了一系列关于有限因子解可能复杂度的结果。此外，该研究解答了[Holroyd et al. Annals of Prob. 2017]提出的三个开放问题，也回应了[Brandt et al. PODC 2017]提出的更一般性问题——后者曾寻求领域（a）与（b）之间的形式化关联。总体而言，我们希望本研究能有助于将这三个视角视为共同的局部性理论的组成部分，这一思路延续了[Bernshteyn 2020+]这篇富有洞见的论文的方向。
英文摘要：
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 of randomized processes, (c) descriptive combinatorics: coming from the area of combinatorics and measure theory. In particular, we study locally checkable labellings in grid graphs from all three perspectives. Most of our results are for the perspective (b) where we prove 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 finitary factor solutions. Among others, it answers three open questions of [Holroyd et al. Annals of Prob. 2017] or the more general question of [Brandt et al. PODC 2017] who asked for a formal connection between the fields (a) and (b). In general, we hope that our treatment will help to view all three perspectives as a part of a common theory of locality, in which we follow the insightful paper of [Bernshteyn 2020+] .
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
