Generateurs algebriques et systemes de paires iterantes

Abstract

The notion of rational transduction is a valuable tool to compare the structures of different languages, in particular context-free languages. The explanation of this is a powerful property of rational transductions with respect to certain iterative pairs [8] and systems of iterative pairs (we define this notion in this paper), in a context-free language. (Intuitively, systems of iterative pairs describe combinations of simultaneous iterative pairs in a context-free language.) This property is the so-called Transfer Theorem, whose terms are: Let A and B be two context-free languages and let T be a rational transduction such that T( B) = A. If A has a strict system of iterative pairs σ, then B has a strict system of iterative pairs σ′, of the same type than σ. (This theorem has been proved in [8] for iterative pairs and we prove it here for systems of iterative pairs.) This theorem means that any combination of certain iterative pairs in the image language by a rational transduction must appear, in a similar way, in the source language. The main result of this paper is obtained by using the previous Transfer Theorem. This result is a characterization of context-free generators i.e. generators of the rational cone or, equivalently [10], of the full-AFL of context-free languages.