We study an extension of the Arrival problem, called Recursive Arrival, inspired by Recursive State Machines, which allows for a family of switching graphs that can call each other in a recursive way. We study the computational complexity of deciding whether a Recursive Arrival instance terminates at a given target vertex. We show this problem is contained in NP \cap coNP, and we show that a search version of the problem lies in UEOPL, and hence in EOPL = PLS \cap PPAD. Furthermore, we show P-hardness of the Recursive Arrival decision problem. By contrast, the current best-known hardness result for Arrival is PL-hardness.

翻译：我们研究Arrival问题的一个扩展形式——递归到达问题（Recursive Arrival），该问题受递归状态机启发，允许一族可相互递归调用的切换图。我们研究判定递归到达实例是否终止于给定目标顶点的计算复杂度。我们证明该问题属于NP ∩ coNP，并且其搜索版本属于UEOPL，因此属于EOPL = PLS ∩ PPAD。此外，我们证明递归到达判定问题具有P-困难性。相比之下，当前Arrival问题已知的最佳困难性结果是PL-困难性。