Composition Closure of Linear Weighted Extended Top-Down Tree Transducers

Linear weighted extended top-down tree transducers with regular look-ahead and with weights from a semiring are formal models that are used in syntax-based statistical machine translation. The composition hierarchies of some restricted versions of such weighted tree transducers (also without regular look-ahead) are considered. In particular, combinations of the restrictions of epsilon-freeness (all rules consume input), nondeletion, and strictness (all rules produce output) are considered. The composition hierarchy is shown to be finite for all but one epsilon-free variant of these weighted transducers over any commutative semiring.