局部路径问题的描述组合学分类
Classification of Local Problems on Paths from the Perspective of Descriptive Combinatorics
摘要：
我们分类的本地问题的输入导向路径有所谓的博雷尔解决方案，并表明这类问题仍然是相同的，如果我们需要一个可测量的解决方案，一个因素的iid解决方案，或解决方案的性质Baire。结合分布式计算领域的工作[Balliu et al. PODC 2019]，描述性组合学领域的工作[Gao et al. arXiv：1803.03872，Bernshteyn arXiv：2004.04905]和随机过程领域的工作[Holroyd et al. Annals of Prob. 2017，Grebík，Rozhoregon arXiv：2103.08394]，这完成了使用这三个领域的复杂性类对有向路径输入的局部问题的分类。一个简单的画面出现了：有四类局部问题，大多数类在所有三个领域都有自然的定义。此外，我们现在知道，随机性\emph{not}有助于解决定向路径上的局部问题。
英文摘要：
We classify which local problems with inputs on oriented paths have so-called Borel solution and show that this class of problems remains the same if we instead require a measurable solution, a factor of iid solution, or a solution with the property of Baire. Together with the work from the field of distributed computing [Balliu et al. PODC 2019], the work from the field of descriptive combinatorics [Gao et al. arXiv:1803.03872, Bernshteyn arXiv:2004.04905] and the work from the field of random processes [Holroyd et al. Annals of Prob. 2017, Grebík, Rozhoň arXiv:2103.08394], this finishes the classification of local problems with inputs on oriented paths using complexity classes from these three fields. A simple picture emerges: there are four classes of local problems and most classes have natural definitions in all three fields. Moreover, we now know that randomness does \emph{not} help with solving local problems on oriented paths.
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