Reachability in succinct and parametric one-counter automata

Christoph Haase, Stephan Kreutzer, Joël Ouaknine, and James Worrell

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 can take the form of 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.

Proceedings of CONCUR 09, LNCS 5710, 2009. 15 pages.

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