The Reachability Problem for Two-Dimensional Vector Addition Systems with States

We prove that the reachability problem for two-dimensional vector addition systems with states is NL-complete or PSPACE-complete, depending on whether numbers in input are encoded unary binary. As a key underlying technical result, we show that, if configuration reachable, then there exists witnessing path whose sequence of transitions contained bounded language defined by regular expression pseudo-polynomially length. This, turn, enables us to lengths minimal witnesses bounded.