Relating Tree Series Transducers and Weighted Tree Automata

Bottom-up tree series transducers (tst) over the semiring A are implemented with the help of bottom-up weighted tree automata (wta) over an extension of A. Therefore bottom-up D-weighted tree automata (D-wta) with D a distributive -algebra are introduced. A D-wta is essentially a wta but uses as transition weight an operation symbol of the -algebra D instead of a semiring element. The given tst is implemented with the help of a D-wta, essentially showing that D-wta are a joint generalization of tst (using IO-substitution) and wta. Then a semiring and a wta are constructed such that the wta computes a formal representation of the semantics of the D-wta. The applicability of the obtained presentation result is demonstrated by deriving a pumping lemma for deterministic finite D-wta from a known pumping lemma for deterministic finite wta. Finally, it is observed that the known decidability results for emptiness cannot be applied to obtain decidability of emptiness for finite D-wta. Thus w...

• Type: Conference
• Year: 2004
• Where: DLT
• Authors: Andreas Maletti
• Keywords: DLT 2004, DLT 2007, Finite D-wta, Pumping Lemma, Tree Automata