Box-Reachability in Vector Addition Systems
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915449356156928 |
|---|---|
| author | Almagor, Shaull Hasson, Itay Pilipczuk, Michał Zaslavski, Michael |
| author_facet | Almagor, Shaull Hasson, Itay Pilipczuk, Michał Zaslavski, Michael |
| contents | We consider a variant of reachability in Vector Addition Systems (VAS) dubbed \emph{box reachability}, whereby a vector $v\in \mathbb{N}^d$ is box-reachable from $0$ in a VAS $V$ if $V$ admits a path from $0$ to $v$ that not only stays in the positive orthant (as in the standard VAS semantics), but also stays below $v$, i.e., within the ``box'' whose opposite corners are $0$ and $v$.
Our main result is that for two-dimensional VAS, the set of box-reachable vertices almost coincides with the standard reachability set: the two sets coincide for all vectors whose coordinates are both above some threshold $W$. We also study properties of box-reachability, exploring the differences and similarities with standard reachability.
Technically, our main result is proved using powerful machinery from convex geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Box-Reachability in Vector Addition Systems Almagor, Shaull Hasson, Itay Pilipczuk, Michał Zaslavski, Michael Formal Languages and Automata Theory We consider a variant of reachability in Vector Addition Systems (VAS) dubbed \emph{box reachability}, whereby a vector $v\in \mathbb{N}^d$ is box-reachable from $0$ in a VAS $V$ if $V$ admits a path from $0$ to $v$ that not only stays in the positive orthant (as in the standard VAS semantics), but also stays below $v$, i.e., within the ``box'' whose opposite corners are $0$ and $v$. Our main result is that for two-dimensional VAS, the set of box-reachable vertices almost coincides with the standard reachability set: the two sets coincide for all vectors whose coordinates are both above some threshold $W$. We also study properties of box-reachability, exploring the differences and similarities with standard reachability. Technically, our main result is proved using powerful machinery from convex geometry. |
| title | Box-Reachability in Vector Addition Systems |
| topic | Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2508.12853 |