Shortest Paths in One-Counter Systems

  • Dmitry Chistikov
  • Wojciech Czerwiński
  • Piotr Hofman
  • Michał Pilipczuk
  • Michael Wehar
Conference paper

DOI: 10.1007/978-3-662-49630-5_27

Volume 9634 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Chistikov D., Czerwiński W., Hofman P., Pilipczuk M., Wehar M. (2016) Shortest Paths in One-Counter Systems. In: Jacobs B., Löding C. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2016. Lecture Notes in Computer Science, vol 9634. Springer, Berlin, Heidelberg

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 \(\mathrm {\Omega }(n^2)\). 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).

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Dmitry Chistikov
    • 1
  • Wojciech Czerwiński
    • 2
  • Piotr Hofman
    • 3
  • Michał Pilipczuk
    • 2
  • Michael Wehar
    • 4
  1. 1.Max Planck Institute for Software Systems (MPI-SWS)Kaiserslautern and SaarbrückenGermany
  2. 2.Institute of InformaticsUniversity of WarsawWarsawPoland
  3. 3.Laboratoire Spécification et Vérification (LSV)ENS Cachan & CNRSParisFrance
  4. 4.Department of Computer Science and EngineeringUniversity at BuffaloBuffaloUSA