English

Deciding Top-Down Determinism of Regular Tree Languages

Formal Languages and Automata Theory 2021-07-08 v1

Abstract

It is well known that for a regular tree language it is decidable whether or not it can be recognized by a deterministic top-down tree automaton (DTA). However, the computational complexity of this problem has not been studied. We show that for a given deterministic bottom-up tree automaton it can be decided in quadratic time whether or not its language can be recognized by a DTA. Since there are finite tree languages that cannot be recognized by DTAs, we also consider finite unions of \DTAs and show that also here, definability within deterministic bottom-up tree automata is decidable in quadratic time.

Keywords

Cite

@article{arxiv.2107.03174,
  title  = {Deciding Top-Down Determinism of Regular Tree Languages},
  author = {Peter Leupold and Sebastian Maneth},
  journal= {arXiv preprint arXiv:2107.03174},
  year   = {2021}
}
R2 v1 2026-06-24T03:57:50.565Z