We consider two natural subclasses of deterministic top-down tree-to-tree transducers, namely, linear and uniform-copying transducers. For both classes we show that it is decidable whether the translation of a transducer with look-ahead can be realized by a transducer without look-ahead. The transducers constructed in this way, may still make use of inspection, i.e., have an additional tree automaton restricting the domain. We provide a second procedure which decides whether inspection can be removed and if so, constructs an equivalent transducer without inspection. The construction relies on a fixpoint algorithm that determines inspection requirements and on dedicated earliest normal forms for linear as well as uniform-copying transducers which can be constructed in polynomial time. As a consequence, equivalence of these transducers can be decided in polynomial time. Applying these results to deterministic bottom-up transducers, we obtain that it is decidable whether or not their translations can be realized by deterministic uniform-copying top-down transducers without look-ahead (but with inspection) - or without both look-ahead and inspection.
@InProceedings{maneth_et_al:LIPIcs.ICALP.2020.134, author = {Maneth, Sebastian and Seidl, Helmut}, title = {{When Is a Bottom-Up Deterministic Tree Translation Top-Down Deterministic?}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {134:1--134:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-138-2}, ISSN = {1868-8969}, year = {2020}, volume = {168}, editor = {Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.134}, URN = {urn:nbn:de:0030-drops-125416}, doi = {10.4230/LIPIcs.ICALP.2020.134}, annote = {Keywords: Top-Down Tree Transducers, Earliest Transformation, Linear Transducers, Uniform-copying Transucers, Removal of Look-ahead, Removal of Inspection} }