The ARRIVIAL problem introduced by Dohrau, G\"artner, Kohler, Matou\v{s}ek and Welzl concerns a train moving on a directed graph proceeding along outward edges according to the position of 'switches' at each vertex, which in turn are toggled whenever the train passes through them. The problem asks whether the train every reaches a designated destination vertex. It is known that ARRIVAL is contained in UP $\cap$ coUP, while the previously best published lower bound is that it is NL-hard. In this note we provide a simple reduction to the $\mathsf{DIGICOMP}_\mathsf{EXP}$ problem considered by Aaronson. It follows in particular that ARRIVAL is both CC-hard and PL-hard.

翻译：Dohrau, G\"Artner, Kohler, Matou\v{s}ek 和 Welzl 提出的快速问题涉及一列列列车在方向图上移动,按照每个顶端的“开关”的位置沿着向外边缘走动,而每个顶端的“开关”的位置,然后在列车通过它们时就被冲动。 问题在于列车是否到达指定目的地的顶端。 众所周知, ARRIVAL 包含在 UP $\ cap coPUP 中, 而先前出版的下限是 NL- hard 。 在本说明中,我们对Aaronson 所考虑的 $mathsf{ DIGICOMP ⁇ mathsf{EXP} $的问题做了简单的削减。 特别是ARRIVAL 是 CC-hard 和 PL-hard 。