Reachability in 3-VAS

Abstract: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.

Computation and Language (cs.CL)

arXiv:2608.04786 [cs.CL]

(or arXiv:2608.04786v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2608.04786 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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