The paper deals with the design of controllers that correct faulty behaviour of sequential machines caused by corrupted inputs. Alternatively, the results can be interpreted as the design of controllers that steer a sequential machine from an unknown initial condition to a prescribed steady-state course. In these terms, the paper characterizes the uncertainties about the initial condition under which the prescribed steady-state course can be achieved. The paper is written within the input/output framework of nonlinear control, and is motivated in part by potential applications to molecular biology.