We study the computational complexity of model checking EF logic and modal logic on parametric one-counter automata (POCA). A POCA is a one-counter automaton whose counter updates are either integer values encoded in binary or integer-valued parameters. Given a formula and a configuration of a POCA, the model-checking problem asks whether the formula is true in this configuration for all possible valuations of the parameters. We show that this problem is undecidable for EF logic via reduction from Hilbert's tenth problem, however for modal logic we prove PSPACE-completeness. Obtaining the PSPACE upper bound involves analysing systems of linear Diophantine inequalities of exponential size that admit solutions of polynomial size. Finally, we show that model checking EF logic on POCA without parameters is PSPACE-complete.
Proceedings of FOSSACS 12, LNCS 7213, 2012. 15 pages.