When is a Bottom-Up Deterministic Tree Translation Top-Down Deterministic?
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915216210526208 |
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| author | Maneth, Sebastian Seidl, Helmut |
| author_facet | Maneth, Sebastian Seidl, Helmut |
| contents | 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 from the same class 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. The procedure relies on a precise abstract interpretation of inspection requirements and a dedicated earliest normal form 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 tree transducers, we obtain that it is decidable whether or not their translations can be realized by deterministic linear or uniform-copying top-down transducers without look-ahead (but with inspection) -- or without both look-ahead and inspection. Look-ahead removal has been known to be a notoriously difficult problem. To the best of our knowledge, this paper is the first to present look-ahead removal for natural and known subclasses of top-down tree transducers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When is a Bottom-Up Deterministic Tree Translation Top-Down Deterministic? Maneth, Sebastian Seidl, Helmut Formal Languages and Automata Theory 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 from the same class 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. The procedure relies on a precise abstract interpretation of inspection requirements and a dedicated earliest normal form 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 tree transducers, we obtain that it is decidable whether or not their translations can be realized by deterministic linear or uniform-copying top-down transducers without look-ahead (but with inspection) -- or without both look-ahead and inspection. Look-ahead removal has been known to be a notoriously difficult problem. To the best of our knowledge, this paper is the first to present look-ahead removal for natural and known subclasses of top-down tree transducers. |
| title | When is a Bottom-Up Deterministic Tree Translation Top-Down Deterministic? |
| topic | Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2503.21329 |