  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.
