Résumé : A generalization from string to trees and from languages to translations is given of the classical result that any regular language can be learned from examples: it is shown that for any deterministic top-down tree transformation there exists a sample set of polynomial size (with respect to the minimal transducer) which allows to infer the translation. Until now, only for string transducers and for simple relabeling tree transducers, similar results had been known. Learning of deterministic top-down tree transducers (DTOPs) is far more involved because a DTOP can copy, delete, and permute its input subtrees. Thus, complex dependencies of labeled input to output paths need to be maintained by the algorithm. First, a Myhill-Nerode theorem is presented for DTOPs, which is interesting on its own. This theorem is then used to construct a learning algorithm for DTOPs. Finally, it is shown how our result can be applied to XML transformations (e.g. XSLT programs). For this, a new DTD-based encoding of unranked trees by ranked ones is presented. Over such encodings, DTOPs can realize many practically interesting XML transformations which cannot be realized on first-child/next-sibling encodings.

A preliminary extended version can be found at http://www.grappa.univ-lille3.fr/~niehren/Papers/learn-dtop/long.pdf .