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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.

68Q45 Formal languages and automata
03B25 Decidability of theories and sets of sentences
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