The Recursive Arrival Problem

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.