Relating tree series transducers and weighted tree automata

Abstract

In this paper we implement bottom-up tree series transducers (tst) over the semiring A with the help of bottom-up weighted tree automata (wta) over an extension of A. Therefore we firstly introduce bottom-up DM-monoid weighted tree automata (DM-wta), which essentially are wta using an operation symbol of a DM-monoid instead of a semiring element as transition weight. Secondly, we show that DM-wta are indeed a generalization of tst (using pure substitution). Thirdly, given a DM-wta we construct a semiring A along with a wta such that the wta computes a formal representation of the semantics of the DM-wta. Finally, we demonstrate the applicability of our presentation result by deriving a pumping lemma for deterministic tst as well as deterministic DM-wta from a pumping lemma for deterministic wta. © Springer-Verlag Berlin Heidelberg 2004.