Survey : Weighted extended top-down tree transducers part I. : basics and expressive power

Weighted extended top-down tree transducers (transducteurs généralisés descendants [Arnold, Dauchet: Bi-transductions de forêts. ICALP'76. Edinburgh University Press, 1976]) received renewed interest in the field of Natural Language Processing, where they are used in syntax-based machine translation. This survey presents the foundations for a theoretical analysis of weighted extended top-down tree transducers. In particular, it discusses essentially complete semirings, which are a novel concept that can be used to lift incomparability results from the unweighted case to the weighted case even in the presence of infinite sums. In addition, several equivalent ways to define weighted extended top-down tree transducers are presented and the individual benefits of each presentation is shown on a small result

Relationally defined clones of tree functions closed under selection or primitive recursion

We investigate classes of tree functions which are closed under composition and primitive recursion or selection (a restricted form of recursion). The main result is the characterization of those finitary relations ς (on the set of all trees of a fixed signature) for which the clone of tree functions preserving ς is closed under selection. Moreover, it turns out that such clones are closed also under primitive recursion