  We study the computational complexity of ARRIVAL, a zero-player game on
$n$-vertex switch graphs introduced by Dohrau, G\"{a}rtner, Kohler,
Matou\v{s}ek, and Welzl. They showed that the problem of deciding termination
of this game is contained in $\text{NP} \cap \text{coNP}$. Karthik C. S.
recently introduced a search variant of ARRIVAL and showed that it is in the
complexity class PLS. In this work, we significantly improve the known upper
bounds for both the decision and the search variants of ARRIVAL.
  First, we resolve a question suggested by Dohrau et al. and show that the
decision variant of ARRIVAL is in $\text{UP} \cap \text{coUP}$. Second, we
prove that the search variant of ARRIVAL is contained in CLS. Third, we give a
randomized $\mathcal{O}(1.4143^n)$-time algorithm to solve both variants.
  Our main technical contributions are (a) an efficiently verifiable
characterization of the unique witness for termination of the ARRIVAL game, and
(b) an efficient way of sampling from the state space of the game. We show that
the problem of finding the unique witness is contained in CLS, whereas it was
previously conjectured to be FPSPACE-complete. The efficient sampling procedure
yields the first algorithm for the problem that has expected runtime
$\mathcal{O}(c^n)$ with $c<2$.

Computational Complexity