Shortest paths in one-counter systems

TL;DR

This paper establishes tight bounds on the length of shortest accepting words and paths in one-counter automata and transition systems, improving understanding of their computational complexity.

Contribution

It provides a tight upper bound of O(n^2) on the shortest accepting words in one-counter automata, closing previous bounds gap.

Findings

Shortest accepting words are at most O(n^2) in length.

Tight bounds are established for shortest paths between configurations.

Results improve theoretical understanding of 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).