Weighted HOM-Problem for Nonnegative Integers

Authors Andreas Maletti , Andreea-Teodora Nász , Erik Paul

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Author Details

Andreas Maletti
  • Institute of Computer Science, Leipzig University, Germany
Andreea-Teodora Nász
  • Institute of Computer Science, Leipzig University, Germany
Erik Paul
  • Institute of Computer Science, Leipzig University, Germany

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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)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantitative automata
  • Theory of computation → Computability
  • Theory of computation → Tree languages
  • Theory of computation → Grammars and context-free languages
  • Weighted Tree Automaton
  • Decision Problem
  • Subtree Equality Constraint
  • Tree Homomorphism
  • HOM-Problem
  • Weighted Tree Grammar
  • Weighted HOM-Problem


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