On-Line Odometers for Two-Sided Symbolic Dynamical Systems

We consider biin nite sequences on a nite alphabet of digits which satisfy a constraint of nite type. Such sequences are perturbed by adding a 1 in position 0. The odometer is the function which transforms the initial sequence into an admissible sequence equivalent to the perturbed one. It is shown that the odometer can be realized by an on-line nite automaton when the constraint is linked to numeration in base , where is a Pisot number satisfying the equation = t1 + +tm , where t1 t2 tm 1 are integers