# Reachability in Two-Dimensional Unary Vector Addition Systems with States is NL-Complete

arXiv: https://arxiv.org/abs/1602.00477 · HTML: https://mlsanity.com/paper/1602.00477/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2016.

## Built on by (most cited first, 1 of 1)

- [Improved Ackermannian lower bound for the Petri nets reachability problem](https://mlsanity.com/paper/2105.08551/) (2021)

## Abstract (arXiv)

Blondin et al. showed at LICS 2015 that two-dimensional vector addition systems with states have reachability witnesses of length exponential in the number of states and polynomial in the norm of vectors. The resulting guess-and-verify algorithm is optimal (PSPACE), but only if the input vectors are given in binary. We answer positively the main question left open by their work, namely establish that reachability witnesses of pseudo-polynomial length always exist. Hence, when the input vectors are given in unary, the improved guess-and-verify algorithm requires only logarithmic space.