English

Checking in Polynomial Time whether or not a Regular Tree Language is Deterministic Top-Down

Formal Languages and Automata Theory 2023-06-02 v1

Abstract

It is well known that for a given bottom-up tree automaton it can be decided whether or not there exists deterministic top-down tree automaton that recognized the same tree language. Recently it was claimed that such a decision can be carried out in polynomial time (Leupold and Maneth, FCT'2021); but their procedure and corresponding property is wrong. Here we correct this mistake and present a correct property which allows to determine in polynomial time whether or not a given tree language can be recognized by a deterministic top-down tree automaton. Furthermore, our new property is stated for arbitrary deterministic bottom-up tree automata, and not for minimal such automata (as before).

Keywords

Cite

@article{arxiv.2306.00573,
  title  = {Checking in Polynomial Time whether or not a Regular Tree Language is Deterministic Top-Down},
  author = {Sebastian Maneth and Helmut Seidl},
  journal= {arXiv preprint arXiv:2306.00573},
  year   = {2023}
}
R2 v1 2026-06-28T10:53:11.628Z