In joint work with John Rhodes (University of California at Berkeley) and Anne Schilling (University of California at Davis), a new approach to random walks on de Bruijn graphs over the alphabet $A$ is developped through right congruences on $A_k$, defined using the natural right action of $A^+$. Right congruences may be approximated by special right congruences, which correspond to semaphore codes and allow an easier computation of the hitting time.