eng
episciences.org
Logical Methods in Computer Science
1860-5974
2019-03-05
Volume 15, Issue 1
10.23638/LMCS-15(1:19)2019
4037
journal article
Shortest paths in one-counter systems
Dmitry Chistikov
Wojciech Czerwiński
Piotr Hofman
Michał Pilipczuk
Michael Wehar
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).
https://lmcs.episciences.org/4037/pdf
Computer Science - Formal Languages and Automata Theory
Computer Science - Logic in Computer Science