Random walks on semaphore codes and delay de Bruijn semigroups

We develop a new approach to random walks on de Bruijn graphs over the alphabet $A$ through right congruences on $A^k$, defined using the natural right action of $A^{+}$. A major role is played by special right congruences, which correspond to semaphore codes and allow an easier computation of the hitting time. We show how right congruences can be approximated by special right congruences.