Transducers for the bidirectional decoding of prefix codes

We construct a transducer for the bidirectional decoding of words encoded by the method introduced by Girod in and we prove that it is bideterministic and that it can be used both for the left-to-right and the right-to-left decoding. We also give a similar construction for a transducer that decodes in both directions words encoded by a generalization of the Girod’s encoding method. We prove that it keeps the same properties of the previous transducer. In addition we show that it has a single initial/final state and that it is minimal.