Reachability in Succinct and Parametric One-Counter Automata
Christoph Haase, Stephan Kreutzer, Joel Ouaknine and James Worrell 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.
infobook title | Proceedings of the 20th International Conference on Concurrency Theory (CONCUR09) |
copyright | Springer-Verlag |
editor | M. Bravetti and G. Zavattaro |
location | Bologna, Italy |
month | September |
pages | 369—383 |
publisher | Springer |
series | Lecture Notes in Computer Science |
volume | 5710 |
year | 2009 |
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