We study complexity classes of local problems on regular trees from the perspective of distributed local algorithms and descriptive combinatorics. We show that, surprisingly, some deterministic local complexity classes from the hierarchy of distributed computing exactly coincide with well studied classes of problems in descriptive combinatorics. Namely, we show that a local problem admits a continuous solution if and only if it admits a local algorithm with local complexity $O(\log^* n)$, and a Baire measurable solution if and only if it admits a local algorithm with local complexity $O(\log n)$.

翻译：我们从分布式本地算法和描述性组合法的角度来研究普通树上复杂的当地问题类别。 我们发现,令人惊讶的是,分布式计算等级中某些决定性的当地复杂类别与精心研究的描述性组合法中的问题类别完全吻合。 也就是说,我们表明,只有当当地问题承认当地复杂的当地算法$O( log) n$( log) 和Baire 的可衡量解决办法,只要它承认当地复杂的当地算法$O( log n) 美元( log n), 并且只有当它承认当地复杂的当地算法$( log n) 的情况下,我们才会承认一种持续的解决办法。