# On reachability in succinct and parameterised one-counter automata

- 11:30 4th March 2009 ( week 7, Hilary Term 2009 )Room 441, Oxford University Computing Laboratory

One-counter automata are a fundamental and widely-studied class of infinite-state systems. In this talk, 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. We 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.

Joint work with Stephan Kreutzer, Joel Ouaknine and James Worrell.