{"title":"关于洗牌和分裂自动机","authors":"Ignacio Mollo Cunningham","doi":"10.1016/j.tcs.2025.115539","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1057 ","pages":"Article 115539"},"PeriodicalIF":1.0000,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On shuffling and splitting automata\",\"authors\":\"Ignacio Mollo Cunningham\",\"doi\":\"10.1016/j.tcs.2025.115539\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>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.</div></div>\",\"PeriodicalId\":49438,\"journal\":{\"name\":\"Theoretical Computer Science\",\"volume\":\"1057 \",\"pages\":\"Article 115539\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2025-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical Computer Science\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0304397525004773\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Computer Science","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304397525004773","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
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.
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.