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Recognizable Transductions , Saturated Transducers and Edit Languages ?

Recognizable transductions constitute a well known, proper subclass of rational transductions. To our knowledge, there has been no characterization of recognizable transductions by a well-defined subclass of transducers. In this work we observe that there is a connection between recognizable transductions and languages consisting of edit strings. More specifically, we define a saturated transducer to be a transducer with the property that, when viewed as an automaton over the edit alphabet, accepts all possible edit strings corresponding to each accepted pair of words. Our main result gives a constructive proof that the class of recognizable transductions coincides with the class of saturated transductions. We also revisit closure properties of recognizable transductions using saturated transducers and discuss the natural role of these objects in edit distance problems.