Shortest paths in one-counter systems

Abstract

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).

28 pages, 2 figures

References in corpus (3)

• Demystifying Reachability in Vector Addition Systems
• Automata and Reduced Words in the Free Group
• Efficient Exact Paths For Dyck and semi-Dyck Labeled Path Reachability