Automata system in finitelly generated groups
D. Gusev, I. A. Ivanov-Pogodaev, A. Kanel-Belov
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.