Shortest paths in one-counter systems
Dmitry V. Chistikov, Wojciech Krzysztof Czerwinski, Piotr Hofman, Michał Pilipczuk, Michael Wehar · Logical Methods in Computer Science · 2019
We show that any one-counter automaton with $n$ states, if its language is non-empty, accepts some word of length at most $O(n^2)$. This closes the gap between the previously known upper bound of $O(n^3)$ and lower bound of $\Omega(n^2)$. More generally, we prove a tight upper bound on the length of shortest paths between arbitrary configurations in one-counter transition systems (weaker bounds have previously appeared in the literature). Comment: 28 pages, 2 figures