全局单计数树自动机

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-06-21 DOI:arxiv-2406.15090

Luisa Herrmann, Richard Mörbitz

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引用次数: 0

摘要

我们引入了全局单计数器树自动机（GOCTA），它与通常的计数器树自动机不同，只对一个计数器工作，计数器按词典顺序穿过树，而不是在每个分支位置重复计数器。我们比较了 GOCTA 和计数树自动机的能力，发现它们的可识别树语言类是不可比的。此外，我们还证明，GOCTA 的空性问题是不可判定的，而与此形成鲜明对比的是，它们的成员资格问题是可判定的。

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Global One-Counter Tree Automata

We introduce global one-counter tree automata (GOCTA) which deviate from usual counter tree automata by working on only one counter which is passed through the tree in lexicographical order, rather than duplicating the counter at every branching position. We compare the capabilities of GOCTA to those of counter tree automata and obtain that their classes of recognizable tree languages are incomparable. Moreover, we show that the emptiness problem of GOCTA is undecidable while, in stark contrast, their membership problem is in P.

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arXiv - CS - Formal Languages and Automata Theory

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