高维自动机的闭包和决策属性

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science Pub Date : 2025-03-03 DOI:10.1016/j.tcs.2025.115156

Amazigh Amrane , Hugo Bazille , Uli Fahrenberg , Krzysztof Ziemiański

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引用次数: 0

摘要

我们报告了一些关于高维自动机（hda）语言理论的进一步发展。hda的正则语言是具有接口的有限区间偏序多集的集合。我们展示了一个抽运引理，它允许我们公开一类非正则语言。关于决定和闭包性质，我们证明了正则语言的包含是可决定的（因此是空的），并且正则语言的交叉点也是规则的。然而，正则语言的补语并不总是正则的。我们引入了一个宽界补，并证明了正则语言的宽界补也是正则的。我们还研究了决定论和歧义。我们证明了规则语言是否被确定性HDA所接受是可决定的，并且存在具有无界歧义的规则语言。最后，我们用最终周期函数来描述单字母确定性语言。

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Closure and decision properties for higher-dimensional automata

We report some further developments regarding the language theory of higher-dimensional automata (HDAs). Regular languages of HDAs are sets of finite interval partially ordered multisets (pomsets) with interfaces. We show a pumping lemma which allows us to expose a class of non-regular languages. Concerning decision and closure properties, we show that inclusion of regular languages is decidable (hence is emptiness), and that intersections of regular languages are again regular. Yet complements of regular languages are not always regular. We introduce a width-bounded complement and show that width-bounded complements of regular languages are again regular.

We also study determinism and ambiguity. We show that it is decidable whether a regular language is accepted by a deterministic HDA and that there exist regular languages with unbounded ambiguity. Finally, we characterize one-letter deterministic languages in terms of ultimately periodic functions.

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来源期刊

Theoretical Computer Science 工程技术-计算机：理论方法

CiteScore

2.60

自引率

18.20%

发文量

471

审稿时长

12.6 months

期刊介绍： Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.