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Deciding Linear Height and Linear Size-To-Height Increase of Macro Tree Transducers

Authors Paul Gallot , Sebastian Maneth, Keisuke Nakano, Charles Peyrat

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Author Details

Paul Gallot
  • Universität Bremen, Germany
Sebastian Maneth
  • Universität Bremen, Germany
Keisuke Nakano
  • Tohoku University, Sendai, Japan
Charles Peyrat
  • ENS Paris-Saclay, France

Funding

This work was partially supported by JSPS KAKENHI Grant Numbers 21K11744 and 22H00520.

Acknowledgements

We thank the anonymous reviewers of a previous version of this paper for their critical comments.

Cite As Get BibTex

Paul Gallot, Sebastian Maneth, Keisuke Nakano, and Charles Peyrat. Deciding Linear Height and Linear Size-To-Height Increase of Macro Tree Transducers. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 138:1-138:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ICALP.2024.138

Abstract

We present a novel normal form for (total deterministic) macro tree transducers (mtts), called "depth proper normal form". If an mtt is in this normal form, then it is guaranteed that each parameter of each state appears at arbitrary depths in the output trees of that state. Intuitively, if some parameter only appears at certain bounded depths in the output trees of a state, then this parameter can be eliminated by in-lining the corresponding output paths at each call site of that state. We use regular look-ahead in order to determine which of the paths should be in-lined. As a consequence of changing the look-ahead, a parameter that was previously appearing at unbounded depths, may be appearing at bounded depths for some new look-ahead; for this reason, our construction has to be iterated to obtain an mtt in depth-normal form. Using the normal form, we can decide whether the translation of an mtt has linear height increase or has linear size-to-height increase.

Subject Classification

ACM Subject Classification
  • Theory of computation → Transducers
Keywords
  • automata
  • formal language theory
  • macro tree transducer
  • normal form

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