On the Boolean Closure of Deterministic Top-Down Tree Automata
Abstract
The class of Boolean combinations of tree languages recognized by deterministic top-down tree automata (also known as deterministic root-to-frontier automata) is studied. The problem of determining for a given regular tree language whether it belongs to this class is open. We provide some progress by two results: First, a characterization of this class by a natural extension of deterministic top-down tree automata is presented, and as an application we obtain a convenient method to show that certain regular tree languages are outside this class. In the second result, it is shown that, for fixed , it is decidable whether a regular tree language is a Boolean combination of tree languages recognized by deterministic top-down tree automata.
Cite
@article{arxiv.2401.06596,
title = {On the Boolean Closure of Deterministic Top-Down Tree Automata},
author = {Christof Löding and Wolfgang Thomas},
journal= {arXiv preprint arXiv:2401.06596},
year = {2024}
}
Comments
This is a preprint of a paper published in a special issue dedicated to the memory of Magnus Steinby in the International Journal of Foundations of Computer Science. Compared to the published journal version, reference [8] has been added in a comment at the end of the introduction