Compositions with Constant Weighted Extended Tree Transducers

Conjecture 11 of [Lagoutte, Maletti: Survey — Weighted extended top-down tree transducers — Part III: Composition. Proc. AFCS, LNCS 7020, p. 272–308, Springer 2011] is confirmed. It is demonstrated that the composition of a constant weighted extended tree transducer with a linear weighted top-down tree transducer can be computed by a single weighted extended tree transducer. Whereas linearity and the top-down property are syntactic, the constant property is semantic. The decidability of the constant property is investigated in several restricted settings.