Lower Bounds for the Reachability Problem in Fixed Dimensional VASSes

@article{Czerwinski2022LowerBF,
  title={Lower Bounds for the Reachability Problem in Fixed Dimensional VASSes},
  author={Wojciech Czerwi'nski and Lukasz Orlikowski},
  journal={Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science},
  year={2022}
}
We study the complexity of the reachability problem for Vector Addition Systems with States (VASSes) in fixed dimensions. We provide four lower bounds improving the currently known state-of-the-art: 1) NP-hardness for unary flat 4-VASSes (VASSes in dimension 4), 2) PSpace-hardness for unary 5-VASSes, 3) ExpSpace-hardness for binary 6-VASSes and 4) Tower-hardness for unary 8-VASSes. 
2 Citations

Long Runs Imply Big Separators in Vector Addition Systems

TLDR
Improved the complexity of the reachability problem (for any subclass) using the separators approach may not be simpler than using the short run approach, and it is proved that a few known examples of involved VASSes fulfil the mentioned conditions.

Involved VASS Zoo

We briefly describe recent advances on understanding the complexity of the reachability problem for vector addition systems (or equivalently for vector addition systems with states - VASSes). We

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