On groups with EDT0L word problem
Group Theory
2026-01-21 v3 Formal Languages and Automata Theory
Abstract
We prove that the word problem for the infinite cyclic group is not EDT0L, and obtain as a corollary that a finitely generated group with EDT0L word problem must be torsion. In addition, we show that the property of having an EDT0L word problem is invariant under change of generating set and passing to finitely generated subgroups. This represents significant progress towards the conjecture that all groups with EDT0L word problem are finite (i.e. precisely the groups with regular word problem).
Cite
@article{arxiv.2505.20057,
title = {On groups with EDT0L word problem},
author = {Alex Bishop and Murray Elder and Alex Evetts and Paul Gallot and Alex Levine},
journal= {arXiv preprint arXiv:2505.20057},
year = {2026}
}
Comments
39 pages (+ 1 page appendix), 3 figures