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arXiv · 2104.13866

Reachability in Vector Addition Systems is Ackermann-complete

Wojciech Czerwiński·Łukasz Orlikowski
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Abstract

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 $\mathcal{F}_k$-hard for Vector Addition Systems with States in dimension $6k$, where $\mathcal{F}_k$ is the $k$-th complexity class from the hierarchy of fast-growing complexity classes.

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Wojciech Czerwiński, Łukasz Orlikowski. 2021-04-28. Reachability in Vector Addition Systems is Ackermann-complete. https://arxiv.org/abs/2104.13866

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