Automata in toposes, and general Myhill-Nerode theorems
Formal Languages and Automata Theory
2023-07-28 v1 Category Theory
Abstract
We extend the functorial approach to automata by Colcombet and Petri\c{s}an [arXiv:1712.07121] from the category of sets to any elementary topos with a natural number object and establish general Myhill-Nerode theorems in our setting. As a special case we recover the result of Boja\'nczyk, Klin and Lasota [arXiv:1402.0897] for orbit-finite nominal automata by considering automata in the Myhill-Schanuel topos of nominal sets.
Keywords
Cite
@article{arxiv.2307.14855,
title = {Automata in toposes, and general Myhill-Nerode theorems},
author = {Victor Iwaniack},
journal= {arXiv preprint arXiv:2307.14855},
year = {2023}
}
Comments
34 pages with appendix. Any comments welcome