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arXiv · 2401.06596

On the Boolean Closure of Deterministic Top-Down Tree Automata

Christof Löding·Wolfgang Thomas
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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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Christof Löding, Wolfgang Thomas. 2024-01-12. On the Boolean Closure of Deterministic Top-Down Tree Automata. https://doi.org/10.1142/s0129054123480015

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