Collectives of Automata in Finitely Generated Groups

Abstract

The present paper is devoted to traversing a maze by a collective of automata. This part of automata theory gave rise to a fairly wide range of diverse problems ([1], [2]), including those related to problems of the theory of computational complexity and probability theory. It turns out that the consideration of complicated algebraic objects, such as Burnside groups, can be interesting in this context. In the paper, we show that the Cayley graph a finitely generated group cannot be traversed by a collective of automata if and only if the group is infinite and its every element is periodic.