Economy of description for single-valued transducers

Decomposing a $k$-valued transducer into $k$ unambiguous ones

“…The first one is that n\ = 1. Then, the uniqueness assumption trivially holds true and can be therefore omitted; the lemma and its proof coincide with [WK95,Prop. 2.1].…”

“…Theorem 2.2 has no special history and is proved by means of pumping methods.In the remainder of this section we prove Theorems 2.1 and 2.2, successively. For the proof of Theorem 2.1 we need the following lemma which strengthens[WK95, Prop. 2.1].…”

When is a functional tree transduction deterministic?

“…For deterministic transducers it does. Here, it corresponds to the notion of "subsequential transducers" for words [2,7,10].…”

“…Corresponding results for word transducers are known at least since [2]. Explicit constructions are described in [7] and [10].…”

“…Especially, we allow these transducers to produce a final pattern after having reached a final state at the root of the input tree. This extension does not enlarge the power of a non-deterministic transducer; in case of a deterministic transducer this notion corresponds to the well-known class or "subsequential transducers" [2,7,10] for words. Section 3 shows that, for every functional transducer we can construct an unambiguous transducer realizing the same transduction.…”