{"title":"Jumping Automata over Infinite Words","authors":"Shaull Almagor, Omer Yizhaq","doi":"10.1007/s00224-024-10192-w","DOIUrl":null,"url":null,"abstract":"<p>Jumping automata are finite automata that read their input in a non-consecutive manner, disregarding the order of the letters in the word. We introduce and study jumping automata over infinite words. Unlike the setting of finite words, which has been well studied, for infinite words it is not clear how words can be reordered. To this end, we consider three semantics: automata that read the infinite word in some order so that no letter is overlooked, automata that can permute the word in windows of a given size k, and automata that can permute the word in windows of an existentially-quantified bound. We study expressiveness, closure properties and algorithmic properties of these models.</p>","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Computing Systems","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s00224-024-10192-w","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Jumping automata are finite automata that read their input in a non-consecutive manner, disregarding the order of the letters in the word. We introduce and study jumping automata over infinite words. Unlike the setting of finite words, which has been well studied, for infinite words it is not clear how words can be reordered. To this end, we consider three semantics: automata that read the infinite word in some order so that no letter is overlooked, automata that can permute the word in windows of a given size k, and automata that can permute the word in windows of an existentially-quantified bound. We study expressiveness, closure properties and algorithmic properties of these models.
跳跃自动机是一种有限自动机，它可以不考虑单词中字母的顺序，以非连续的方式读取输入内容。我们介绍并研究无限词上的跳跃自动机。与有限单词的研究不同，对于无限单词，单词如何重新排序尚不清楚。为此，我们考虑了三种语义：按一定顺序读取无限词以便不忽略任何字母的自动机、能在给定大小为 k 的窗口中排列词的自动机，以及能在存在量化约束的窗口中排列词的自动机。我们将研究这些模型的表现力、闭合特性和算法特性。
期刊介绍：
TOCS is devoted to publishing original research from all areas of theoretical computer science, ranging from foundational areas such as computational complexity, to fundamental areas such as algorithms and data structures, to focused areas such as parallel and distributed algorithms and architectures.
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