发表机构
University of Warsaw（华沙大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究确定了2-4维向量加法系统（VAS）可达性问题的复杂度，证明三维对称VAS（3-VAS）的可达性问题为PSPACE难，结合已有上界得出3-VAS、4-VAS及其对称片段的该问题是PSPACE完全。
AI 中文摘要
我们确定了固定低维下（无状态）向量加法系统（VAS）中可达性问题的确切复杂度。在2-4维中，该问题仅已知介于NP和PSPACE之间。我们证明了三维对称向量加法系统（3-VAS，是一般3-VAS的受限片段）的可达性问题是PSPACE难的。结合先前已确立的PSPACE上界，我们的结果确定了3-VAS、4-VAS及其对称片段的该问题复杂度为PSPACE完全。
英文摘要
We settle the exact complexity of the reachability problem in (stateless) vector addition systems (VAS) in fixed low dimension. In dimensions 2-4 it has only been known to be sandwiched between NP and PSPACE. We prove PSPACE-hardness of the reachability problem for symmetric vector addition systems in dimension 3 (3-VAS), a restricted fragment of general 3-VAS. Combined with previously established PSPACE upper bounds, our result settles the complexity of the problem to be PSPACE-complete in 3-VAS and 4-VAS, as well as in their symmetric fragments.
