Reachability in 3-VAS
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.
| Authors | Łukasz Kamiński, Sławomir Lasota |
|---|---|
| Primary category | cs.CL |
| Published | 5 August 2026 |
| Last updated at source | 5 August 2026 |
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