2023/10/13 by Wojciech Czerwiński, Czerwiński, Wojciech, Ismaël Jecker +7
Computer Science · #Complexity and Algorithms in Graphs #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Logic in Computer Science (cs.LO) #Machine Learning and Algorithms #Quantum Computing Algorithms and Architecture
paper · pdf · doi:10.48550/arxiv.2310.09008
openalex publication_date 2023/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Fk-hard for VASS of dimension 3k+2 (the complexity class Fk 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: Fk-hardness in dimension 2k+3. Furthermore, building on our new insights we show a new lower bound for pushdown VASS: Fk-hardness in dimension \frac k 2 + 4. 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).