Decidability of weak simulation on one-counter nets

One-counter nets (OCN) are Petri nets with exactly one unbounded place. They are equiv-alent to a subclass of one-counter automata with only a weak test for zero. We show that weak simulation preorder is decidable for OCN and that weak simulation approximants do not converge at level ω, but only at ω2. In contrast, other semantic relations like weak bisimulation are undecidable for OCN [17], and so are weak (and strong) trace inclusion (Sec. 7).