2026-08-05T23:18:26Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:19408 2024-03-06T11:03:58Z ddc:004 open_access

New Lower Bounds for Reachability in Vector Addition Systems Czerwiński, Wojciech Jecker, Ismaël Lasota, Sławomir Leroux, Jérôme Orlikowski, Łukasz vector addition systems reachability problem pushdown vector addition system lower bounds We investigate the dimension-parametric complexity of the reachability problem in vector addition systems with states (VASS) and its extension with pushdown stack (pushdown VASS). Up to now, the problem is known to be F_d-hard for VASS of dimension 3d+2 (the complexity class F_d corresponds to the kth level of the fast-growing hierarchy), and no essentially better bound is known for pushdown VASS. We provide a new construction that improves the lower bound for VASS: F_d-hardness in dimension 2d+3. Furthermore, building on our new insights we show a new lower bound for pushdown VASS: F_d-hardness in dimension d/2 + 6. This dimension-parametric lower bound is strictly stronger than the upper bound for VASS, which suggests that the (still unknown) complexity of the reachability problem in pushdown VASS is higher than in plain VASS (where it is Ackermann-complete). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Wojciech Czerwiński and Ismaël Jecker and Sławomir Lasota and Jérôme Leroux and Łukasz Orlikowski 2023 Is Part Of LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2023.35 urn:nbn:de:0030-drops-194088 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.35 eng https://creativecommons.org/licenses/by/4.0/legalcode