Automata system in finitelly generated groups
Group Theory
2026-03-10 v3 Logic
Abstract
We prove that any finite system of interacted automata can not leave some finite arear of Calley graph of periodic group. If group has non-periodic element, then its Calley graph can be explored by some finite automata with 3 pebbles. If group is finitely generated and aperiodic then it can not be explored by any system of finite automata.
Cite
@article{arxiv.1812.00716,
title = {Automata system in finitelly generated groups},
author = {D. Gusev and I. A. Ivanov-Pogodaev and A. Kanel-Belov},
journal= {arXiv preprint arXiv:1812.00716},
year = {2026}
}
Comments
12 pages, in Russian, supported by Russian Science Foundation, grant No 17-11-01377