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.
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}
}