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Equivalence of finite-valued tree transducers is decidable. (English) Zbl 0809.68087
Summary: A bottom-up finite state tree transducer (FST) $$M$$ is called $$k$$-valued iff for every input tree there are at most $$k$$ different output trees. $$M$$ is called finite-valued iff it is $$k$$-valued for some $$k$$. We show that it is decidable for every $$k$$ whether or not a given FST $$M$$ is $$k$$- valued. We give an effective characterization of all finite-valued FSTs and derive a (sharp) upper bound for the valuedness provided it is finite. We decompose a finite-valued FST $$M$$ into a finite number of single-valued FSTs. This enables us to prove: it is decidable whether or not the translation of an FST $$M$$ is included in the translation of a finite-valued FST $$M'$$. We also consider these questions for size- valuedness.

##### MSC:
 68Q45 Formal languages and automata 03B25 Decidability of theories and sets of sentences
##### Keywords:
bottom-up finite state tree transducer
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##### References:
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