Pseudoperiodic Words and a Question of Shevelev

We generalize the familiar notion of periodicity in sequences to a new kind of pseudoperiodicity, and we prove some basic results about it. We revisit the results of a 2012 paper of Shevelev and reprove his results in a simpler and more unified manner, and provide a complete answer to one of his pre...

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Main Authors: Joseph Meleshko, Pascal Ochem, Jeffrey Shallit, Sonja Linghui Shan
Format: Article
Language:English
Published: Discrete Mathematics & Theoretical Computer Science 2023-10-01
Series:Discrete Mathematics & Theoretical Computer Science
Subjects:
Online Access:http://dmtcs.episciences.org/9919/pdf
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author Joseph Meleshko
Pascal Ochem
Jeffrey Shallit
Sonja Linghui Shan
author_facet Joseph Meleshko
Pascal Ochem
Jeffrey Shallit
Sonja Linghui Shan
author_sort Joseph Meleshko
collection DOAJ
description We generalize the familiar notion of periodicity in sequences to a new kind of pseudoperiodicity, and we prove some basic results about it. We revisit the results of a 2012 paper of Shevelev and reprove his results in a simpler and more unified manner, and provide a complete answer to one of his previously unresolved questions. We consider finding words with specific pseudoperiod and having the smallest possible critical exponent. Finally, we consider the problem of determining whether a finite word is pseudoperiodic of a given size, and show that it is NP-complete.
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publisher Discrete Mathematics & Theoretical Computer Science
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spelling doaj-art-95a9b9f94eb54458bd28dcee338490672025-08-20T01:49:32ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502023-10-01vol. 25:2Automata, Logic and Semantics10.46298/dmtcs.99199919Pseudoperiodic Words and a Question of ShevelevJoseph MeleshkoPascal OchemJeffrey ShallitSonja Linghui ShanWe generalize the familiar notion of periodicity in sequences to a new kind of pseudoperiodicity, and we prove some basic results about it. We revisit the results of a 2012 paper of Shevelev and reprove his results in a simpler and more unified manner, and provide a complete answer to one of his previously unresolved questions. We consider finding words with specific pseudoperiod and having the smallest possible critical exponent. Finally, we consider the problem of determining whether a finite word is pseudoperiodic of a given size, and show that it is NP-complete.http://dmtcs.episciences.org/9919/pdfmathematics - combinatoricscomputer science - discrete mathematicscomputer science - formal languages and automata theory
spellingShingle Joseph Meleshko
Pascal Ochem
Jeffrey Shallit
Sonja Linghui Shan
Pseudoperiodic Words and a Question of Shevelev
Discrete Mathematics & Theoretical Computer Science
mathematics - combinatorics
computer science - discrete mathematics
computer science - formal languages and automata theory
title Pseudoperiodic Words and a Question of Shevelev
title_full Pseudoperiodic Words and a Question of Shevelev
title_fullStr Pseudoperiodic Words and a Question of Shevelev
title_full_unstemmed Pseudoperiodic Words and a Question of Shevelev
title_short Pseudoperiodic Words and a Question of Shevelev
title_sort pseudoperiodic words and a question of shevelev
topic mathematics - combinatorics
computer science - discrete mathematics
computer science - formal languages and automata theory
url http://dmtcs.episciences.org/9919/pdf
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AT pascalochem pseudoperiodicwordsandaquestionofshevelev
AT jeffreyshallit pseudoperiodicwordsandaquestionofshevelev
AT sonjalinghuishan pseudoperiodicwordsandaquestionofshevelev