Determinacy and Subsumption for Single-Valued Bottom-Up Tree Transducers

This paper discusses the decidability of determinacy and subsumption for tree transducers. For two tree transducers T1 and T2, T1 determines T2 if the output of T2 is identified by the output of T1, that is, there is a partial function f such that [[T2]] = f ◦ [[T1]] where [[T1]] and [[T2]] are tree transformation relations induced by T1 and T2, respectively. Also, T1 subsumes T2 if T1 determines T2 and the partial function f such that [[T2]] = f◦[[T1]] can be defined by a transducer in a designated class that T2 belongs to. In this paper, we show that determinacy is decidable for single-valued linear extended bottom-up tree transducers as the determiner class and single-valued bottom-up tree transducers as the determinee class. We also show that subsumption is decidable for these classes.