Group-Walking Automata - Ville Salo; Ilkka Törmä (Berlin, 2022)
In the setting of symbolic dynamics on discrete finitely generated infinite groups, we define a model of multi-headed finite automata that walk on Cayley graphs, and use it to define subshifts. We characterize the torsion groups (also known as periodic groups) as those on which the group-walking automata are strictly weaker than Turing machines.
Cellular Automata and Discrete Complex Systems