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Ban, JC., Chang, CH. & Wu, YL. Decidability of CPC-irreducibility of subshifts of finite type over free groups. Semigroup Forum 106, 527–542 (2023).

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
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.5 MB)
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Language: English
Published: Springer Nature, 2023
Publish Date: 2023-08-17


This 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.

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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
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: Open Access funding provided by University of Oulu including Oulu University Hospital.
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