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.

翻译：矢量添加系统和等效的Peteri 网是公认的同值货币模型。对于具有长期研究历史的矢量添加系统来说,核心算法问题是可触及性问题,即从一个配置到另一个配置是否存在运行。我们解决它的复杂程度,即Ackermann完成,从而解决45年来尚未解决的问题。我们尤其证明,对于具有6k$的国家的矢量添加系统来说,问题在于$\mathcal{F ⁇ k$-hard, 在那里,$\mathcal{F ⁇ k$是快速增长的复杂等级中第一级1k$-k$的复杂程度。