# New Pumping Technique for 2-dimensional VASS

## TL;DR

This paper introduces a novel geometric pumping technique for 2-dimensional VASS, enabling new bounds and lemmas that could impact decidability and language analysis.

## Contribution

It presents a new geometric pumping method for 2-VASS, providing a fresh approach to analyzing their language properties and bounds.

## Key findings

- Reproved exponential bound on shortest accepting run length
- Proved a new pumping lemma for 2-VASS languages
- Potential applications in decidability and regular separability

## Abstract

We propose a new pumping technique for 2-dimensional vector addition systems with states (2-VASS) building on natural geometric properties of runs. We illustrate its applicability by reproving an exponential bound on the length of the shortest accepting run, and by proving a new pumping lemma for languages of 2-VASS. The technique is expected to be useful for settling questions concerning languages of 2-VASS, e.g., for establishing decidability status of the regular separability problem.