# Fast Computations on Ordered Nominal Sets (extended version)

6 Sep 2022

David Venhoek, Joshua Moerman and Jurriaan Rot

TCS

This is an extended version of our ICTAC’18 paper.

## Abstract

Nominal automata are models for recognising languages over infinite alphabets, based on the algebraic notion of *nominal set*.
Motivated by their use in automata theory, we show how to compute efficiently with nominal sets over the so-called *total order symmetry,* a variant which allows to compare alphabet letters for equality as well as their respective order.
We develop an explicit finite representation of such nominal sets and basic constructions thereon.
The approach is implemented as the library Ons (Ordered Nominal Sets), enabling programming with infinite sets. Returning to our motivation of nominal automata, 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.

## Links

arXiv

doi: 10.1016/j.tcs.2022.09.002

C++ Implementation

Haskell Implementation