Internship Report Compositions of Extended Top-down Tree Transducers

Many aspects of machine translation of natural languages can be formalized by employing weighted finite-state (string) transducers [22, 40]. Successful implementations based on this wordor phrasebased approach are, for example, the At&t Fsm toolkit [41], Xerox’s finite-state calculus [24], the Rwth toolkit [23], Carmel [19], and OpenFst [2]. However, the phrase-based approach is not expressive enough, for example, to easily handle the rotation needed in the translation of the English structure NP-V-NP (subject-verb-noun phrase) to the Arabic structure V-NP-NP. A finitestate transducer can only implement this rotation by storing the subject, which might be very long, in its finite memory. Syntax-based (or tree-based) formalisms can remedy this shortage. An example of such formalisms is the top-down tree transducer [42, 43], of which a weighted version is implemented in the toolkit Tiburon [38], together with some standard operations. Those weighted top-down tree transducers [29, 14, 17] (also called ‘tree series transducers’) are a joint generalization of the unweighted top-down tree transducer (tdtt) [42, 43] and the weighted tree automaton [7, 10, 1, 27, 16, 9, 8]. During my internship, I investigated compositions of weighted and unweighted extended topdown tree transducers. An unweighted tree transducer computes a relation τ between input and output trees, and a weighted tree transducer computes a weighted relation between input and output trees (i.e., it assigns a weight to each pair of input and output trees). An unweighted tree transducer can be seen as a weighted tree transducer, where the weighted relation assigns true (resp. false) to a pair of trees if this pair is (resp. is not) in the relation τ . Using the real numbers as weight structure, we compose two weighted relations τ1 : A × B → IR and τ2 : B × C → IR by requiring that (τ1 ; τ2)(a, c) = ∑