# Linear Equations with Ordered Data

arXiv: https://arxiv.org/abs/1802.06660 · HTML: https://mlsanity.com/paper/1802.06660/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2018.

## Built on by (most cited first, 2 of 2)

- [Improved Ackermannian lower bound for the Petri nets reachability problem](https://mlsanity.com/paper/2105.08551/) (2021)
- [Solvability of orbit-finite systems of linear equations](https://mlsanity.com/paper/2201.09060/) (2022)

## Abstract (arXiv)

Following a recently considered generalization of linear equations to unordered data vectors, we perform a further generalization to ordered data vectors. These generalized equations naturally appear in the analysis of vector addition systems (or Petri nets) extended with ordered data. We show that nonnegative-integer solvability of linear equations is computationally equivalent (up to an exponential blowup) with the reachability problem for (plain) vector addition systems. This high complexity is surprising, and contrasts with NP-completeness for unordered data vectors. Also surprisingly, we achieve polynomial time complexity of the solvability problem when the nonnegative-integer restriction on solutions is dropped.