On the Boolean Closure of Deterministic Top-Down Tree Automata
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910295340875776 |
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| author | Löding, Christof Thomas, Wolfgang |
| author_facet | Löding, Christof Thomas, Wolfgang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06596 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Boolean Closure of Deterministic Top-Down Tree Automata Löding, Christof Thomas, Wolfgang Formal Languages and Automata Theory F.4.3; F.1.1 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. |
| title | On the Boolean Closure of Deterministic Top-Down Tree Automata |
| topic | Formal Languages and Automata Theory F.4.3; F.1.1 |
| url | https://arxiv.org/abs/2401.06596 |