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Decidability of CPC-irreducibility of subshifts of finite type over free groups |
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| Author: | Ban, Jung-Chao1,2; Chang, Chih-Hung3; Wu, Yu-Liang4 |
| Organizations: |
1Department of Mathematical Sciences, National Chengchi University, Taipei, 11605, Taiwan, ROC 2Mathematics Division, National Center for Theoretical Science, National Taiwan University, Taipei, 10617, Taiwan, ROC 3Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung, 81148, Taiwan, ROC
4Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, 90014, Oulu, Finland
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| Format: | article |
| Version: | published version |
| Access: | open |
| Online Access: | PDF Full Text (PDF, 0.5 MB) |
| Persistent link: | http://urn.fi/urn:nbn:fi-fe2023081797492 |
| Language: | English |
| Published: |
Springer Nature,
2023
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| Publish Date: | 2023-08-17 |
| Description: |
AbstractThis paper attempts to study the irreducibility on complete prefix code (CPC-irreducibility) of a Markov shift over a free group, a topological mixing property first considered for shift spaces over free semigroups that induces chaotic behavior such as the existence of a dense set of periodic points. An example shows that the (d,c)-reduction, an effective algorithm of determination of CPC-irreducibility of Markov shifts over free semigroups (Ban et al. in J Stat Phys 177:1043–1062, 2019), fails for general Markov shifts over free groups. This paper reveals an algorithm for determining the CPC-irreducibility of Markov shifts over both free semigroups and groups. Furthermore, such an examination is finitely checkable, and an upper bound for the complexity of the algorithm is provided. see all
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| Series: |
Semigroup forum |
| ISSN: | 0037-1912 |
| ISSN-E: | 1432-2137 |
| ISSN-L: | 0037-1912 |
| Volume: | 106 |
| Issue: | 3 |
| Pages: | 527 - 542 |
| DOI: | 10.1007/s00233-023-10360-3 |
| OADOI: | https://oadoi.org/10.1007/s00233-023-10360-3 |
| Type of Publication: |
A1 Journal article – refereed |
| Field of Science: |
111 Mathematics |
| Subjects: | |
| Funding: |
Open Access funding provided by University of Oulu including Oulu University Hospital. |
| Copyright information: |
© The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
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https://creativecommons.org/licenses/by/4.0/ |