This draft is a follow-up of the Ackermannian lower bound for the reachability problem in vector addition systems with states (VASS), recently announced by Czerwi\'nski and Orlikowski. Independently, the same result has been announced by Leroux, but with a significantly different proof. We provide a simplification of the former construction, thus improving the lower bound for VASS in fixed dimension: while Czerwi\'nski and Orlikowski prove $F_k$-hardness in dimension $6k$, and Leroux in dimension $4k+9$, the simplified construction yields $F_k$-hardness already in dimension $3k+2$.

中文翻译：

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针对VASS可达性问题的改进的阿克曼下界

该草案是Czerwi'nski和Orlikowski最近宣布的带状态向量加法系统（VASS）中的可达性问题的阿克曼下界的后续操作。独立地，Leroux宣布了相同的结果，但有明显不同的证明。我们简化了以前的结构，从而提高了固定维数下VASS的下限：虽然Czerwi'nski和Orlikowski证明维数为$ F_k $-硬度为$ 6k $，而Leroux维数为$ 4k + 9 $，但是简化的结构会产生$ F_k $-已经在$ 3k + 2 $维度上的硬度。