A full Mealy automaton is associated with a graph and a square complex, which contains an anti-torus if and only if the automaton is bi-reversible and the graph is aperiodic.
problem Determining the existence of anti-tori in square complexes associated with Mealy automata
method Associating a graph and a square complex with a Mealy automaton and proving the equivalence between bi-reversibility and aperiodicity of the graph
result The square complex contains an anti-torus if and only if the automaton is bi-reversible and the graph is aperiodic