On the Insufficiency of Surface Data for the Learning of Transformational Languages

Identifiability in the limit is studied, with special reference to transformational languages on a given base. First a theorem is proved which gives necessary conditions for a class of languages to be identifiable in the limit. With added assumptions, these conditions become sufficient for identifiability. The question of whether the class of transformational languages on a fixed context-free base is identifiable is studied. Counterexamples, that is, context-free grammars for which the set of transformational languages is not identifiable, are exhibited. One of these examples involves no deletion, the use of the transformational cycle and only binary transformations.