关于洗牌和分裂自动机

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-07-02 DOI:arxiv-2407.02660

Ignacio Mollo Cunningham

{"title":"关于洗牌和分裂自动机","authors":"Ignacio Mollo Cunningham","doi":"arxiv-2407.02660","DOIUrl":null,"url":null,"abstract":"We consider a class of finite state three-tape transducers which models the\noperation of shuffling and splitting words. We present them as automata over\nthe so-called Shuffling Monoid. These automata can be seen as either shufflers\nor splitters interchangeably. We prove that functionality is decidable for\nsplitters, and we also show that the equivalence between functional splitters\nis decidable. Moreover, in the deterministic case, the algorithm for\nequivalence is polynomial on the number of states of the splitter.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"39 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Shuffling and Splitting Automata\",\"authors\":\"Ignacio Mollo Cunningham\",\"doi\":\"arxiv-2407.02660\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a class of finite state three-tape transducers which models the\\noperation of shuffling and splitting words. We present them as automata over\\nthe so-called Shuffling Monoid. These automata can be seen as either shufflers\\nor splitters interchangeably. We prove that functionality is decidable for\\nsplitters, and we also show that the equivalence between functional splitters\\nis decidable. Moreover, in the deterministic case, the algorithm for\\nequivalence is polynomial on the number of states of the splitter.\",\"PeriodicalId\":501124,\"journal\":{\"name\":\"arXiv - CS - Formal Languages and Automata Theory\",\"volume\":\"39 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Formal Languages and Automata Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.02660\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Formal Languages and Automata Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.02660","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们考虑了一类有限状态三带转换器，它模拟了洗牌和拆字的操作。我们将它们作为所谓的 "洗牌单体"（Shuffling Monoid）上的自动机来介绍。这些自动机可以被看作是洗牌器，也可以被看作是拆字器。我们证明了分词器的功能性是可解的，还证明了功能性分词器之间的等价性是可解的。此外，在确定性情况下，等价性的算法是分裂器状态数的多项式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On Shuffling and Splitting Automata

We consider a class of finite state three-tape transducers which models the operation of shuffling and splitting words. We present them as automata over the so-called Shuffling Monoid. These automata can be seen as either shufflers or splitters interchangeably. We prove that functionality is decidable for splitters, and we also show that the equivalence between functional splitters is decidable. Moreover, in the deterministic case, the algorithm for equivalence is polynomial on the number of states of the splitter.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - CS - Formal Languages and Automata Theory

自引率

0.00%

发文量