Relating tree series transducers and weighted tree automata

Authors:
Andreas Maletti
Affiliations:
Fakultät Informatik, Technische Universität Dresden, Dresden, Germany
Venue:
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
Year:
2004

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Abstract

In this paper we implement bottom-up tree series transducers (tst) over the semiring $\mathcal{A}$ with the help of bottom-up weighted tree automata (wta) over an extension of $\mathcal{A}$. 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 $\mathcal{A}$ 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.