Reachability in Succinct and Parametric One-Counter Automata

  • Authors:

  • Christoph Haase;Stephan Kreutzer;Joël Ouaknine;James Worrell

  • Affiliations:

  • Computing Laboratory, Oxford University, UK;Computing Laboratory, Oxford University, UK;Computing Laboratory, Oxford University, UK;Computing Laboratory, Oxford University, UK

  • Venue:
  • CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
  • Year:
  • 2009

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Abstract

One-counter automata are a fundamental and widely-studied class of infinite-state systems. In this paper we consider one-counter automata with counter updates encoded in binary--which we refer to as the succinct encoding. It is easily seen that the reachability problem for this class of machines is in PSpace and is NP -hard. One of the main results of this paper is to show that this problem is in fact in NP , and is thus NP -complete. We also consider parametric one-counter automata, in which counter updates be integer-valued parameters. The reachability problem asks whether there are values for the parameters such that a final state can be reached from an initial state. Our second main result shows decidability of the reachability problem for parametric one-counter automata by reduction to existential Presburger arithmetic with divisibility.