J. Cassaigne, J. Karhumäki, S. Puzynina, Markus A. Whiteland
{"title":"k-Abelian等价与合理性","authors":"J. Cassaigne, J. Karhumäki, S. Puzynina, Markus A. Whiteland","doi":"10.3233/FI-2017-1553","DOIUrl":null,"url":null,"abstract":"Two words u and v are said to be k-abelian equivalent if, for each word x of length at most k, the number of occurrences of x as a factor of u is the same as for v. We study some combinatorial properties of k-abelian equivalence classes. Our starting point is a characterization of k-abelian equivalence by rewriting, so-called k-switching. We show that the set of lexicographically least representatives of equivalence classes is a regular language. From this we infer that the sequence of the numbers of equivalence classes is $$\\mathbb {N}$$-rational. We also show that the set of words defining k-abelian singleton classes is regular.","PeriodicalId":56310,"journal":{"name":"Fundamenta Informaticae","volume":"15 1","pages":"77-88"},"PeriodicalIF":0.4000,"publicationDate":"2016-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"k-Abelian Equivalence and Rationality\",\"authors\":\"J. Cassaigne, J. Karhumäki, S. Puzynina, Markus A. Whiteland\",\"doi\":\"10.3233/FI-2017-1553\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Two words u and v are said to be k-abelian equivalent if, for each word x of length at most k, the number of occurrences of x as a factor of u is the same as for v. We study some combinatorial properties of k-abelian equivalence classes. Our starting point is a characterization of k-abelian equivalence by rewriting, so-called k-switching. We show that the set of lexicographically least representatives of equivalence classes is a regular language. From this we infer that the sequence of the numbers of equivalence classes is $$\\\\mathbb {N}$$-rational. We also show that the set of words defining k-abelian singleton classes is regular.\",\"PeriodicalId\":56310,\"journal\":{\"name\":\"Fundamenta Informaticae\",\"volume\":\"15 1\",\"pages\":\"77-88\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2016-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fundamenta Informaticae\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.3233/FI-2017-1553\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamenta Informaticae","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.3233/FI-2017-1553","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
Two words u and v are said to be k-abelian equivalent if, for each word x of length at most k, the number of occurrences of x as a factor of u is the same as for v. We study some combinatorial properties of k-abelian equivalence classes. Our starting point is a characterization of k-abelian equivalence by rewriting, so-called k-switching. We show that the set of lexicographically least representatives of equivalence classes is a regular language. From this we infer that the sequence of the numbers of equivalence classes is $$\mathbb {N}$$-rational. We also show that the set of words defining k-abelian singleton classes is regular.
期刊介绍:
Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing:
solutions by mathematical methods of problems emerging in computer science
solutions of mathematical problems inspired by computer science.
Topics of interest include (but are not restricted to):
theory of computing,
complexity theory,
algorithms and data structures,
computational aspects of combinatorics and graph theory,
programming language theory,
theoretical aspects of programming languages,
computer-aided verification,
computer science logic,
database theory,
logic programming,
automated deduction,
formal languages and automata theory,
concurrency and distributed computing,
cryptography and security,
theoretical issues in artificial intelligence,
machine learning,
pattern recognition,
algorithmic game theory,
bioinformatics and computational biology,
quantum computing,
probabilistic methods,
algebraic and categorical methods.