Computer Science > Formal Languages and Automata Theory
[Submitted on 12 Jan 2024]
Title:On the Boolean Closure of Deterministic Top-Down Tree Automata
View PDF HTML (experimental)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 $k$, it is decidable whether a regular tree language is a Boolean combination of $k$ tree languages recognized by deterministic top-down tree automata.
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