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DOI: 10.4230/LIPIcs.STACS.2024.51
Weighted HOM-Problem for Nonnegative Integers

Authors: Andreas Maletti, Andreea-Teodora Nász, and Erik Paul

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
The HOM-problem asks whether the image of a regular tree language under a given tree homomorphism is again regular. It was recently shown to be decidable by Godoy, Giménez, Ramos, and Àlvarez. In this paper, the ℕ-weighted version of this problem is considered and its decidability is proved. More precisely, it is decidable in polynomial time whether the image of a regular ℕ-weighted tree language under a nondeleting, nonerasing tree homomorphism is regular.
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Andreas Maletti, Andreea-Teodora Nász, and Erik Paul. Weighted HOM-Problem for Nonnegative Integers. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 51:1-51:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{maletti_et_al:LIPIcs.STACS.2024.51,
  author =	{Maletti, Andreas and N\'{a}sz, Andreea-Teodora and Paul, Erik},
  title =	{{Weighted HOM-Problem for Nonnegative Integers}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{51:1--51:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.51},
  URN =		{urn:nbn:de:0030-drops-197614},
  doi =		{10.4230/LIPIcs.STACS.2024.51},
  annote =	{Keywords: Weighted Tree Automaton, Decision Problem, Subtree Equality Constraint, Tree Homomorphism, HOM-Problem, Weighted Tree Grammar, Weighted HOM-Problem}
}
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