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.
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Maletti, A. (2004). Relating Tree Series Transducers and Weighted Tree Automata. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds) Developments in Language Theory. DLT 2004. Lecture Notes in Computer Science, vol 3340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30550-7_27
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DOI: https://doi.org/10.1007/978-3-540-30550-7_27
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