Simulation Problems Over One-Counter Nets

This is a journal version of papers HMT2013 and HLMT2013.

One-counter nets (OCN) are finite automata equipped with a counter that can store non-negative integer values, and that cannot be tested for zero. Equivalently, these are exactly \(1\)-dimensional vector addition systems with states. We show that both strong and weak simulation preorder on OCN are PSPACE-complete.