Michael Blondin, Matthias Englert, A. Finkel, Stefan Göller, C. Haase, R. Lazic, P. McKenzie, Patrick Totzke
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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 the numbers in the input are encoded in unary or binary. As a key underlying technical result, we show that, if a configuration is reachable, then there exists a witnessing path whose sequence of transitions is contained in a bounded language defined by a regular expression of pseudo-polynomially bounded length. This, in turn, enables us to prove that the lengths of minimal reachability witnesses are pseudo-polynomially bounded.
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