# Fast Computations on Ordered Nominal Sets

arXiv: https://arxiv.org/abs/1902.08414 · HTML: https://mlsanity.com/paper/1902.08414/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2019.

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

- [Learning Canonical Register Automata over Ordered Data Domains](https://mlsanity.com/paper/2608.18765/) (2026)

## Abstract (arXiv)

We show how to compute efficiently with nominal sets over the total order symmetry, by developing a direct representation of such nominal sets and basic constructions thereon. In contrast to previous approaches, we work directly at the level of orbits, which allows for an accurate complexity analysis. The approach is implemented as the library ONS (Ordered Nominal Sets). Our main motivation is nominal automata, which are models for recognising languages over infinite alphabets. We evaluate ONS in two applications: minimisation of automata and active automata learning. In both cases, ONS is competitive compared to existing implementations and outperforms them for certain classes of inputs.