Reachability in Vector Addition Systems is Ackermann-complete

04/28/2021

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by   Wojciech Czerwiński, et al.

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Vector Addition Systems and equivalent Petri nets are a well established models of concurrency. The central algorithmic problem for Vector Addition Systems with a long research history is the reachability problem asking whether there exists a run from one given configuration to another. We settle its complexity to be Ackermann-complete thus closing the problem open for 45 years. In particular we prove that the problem is ℱ_k-hard for Vector Addition Systems with States in dimension 6k, where ℱ_k is the k-th complexity class from the hierarchy of fast-growing complexity classes.