Automata system in finitelly generated groups

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.

arXiv comment12 pages, in Russian, supported by Russian Science Foundation, grant No 17-11-01377