Decidability of CPC-irreducibility of subshifts of finite type over free groups
|Author:||Ban, Jung-Chao1,2; Chang, Chih-Hung3; Wu, Yu-Liang4|
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
|Online Access:||PDF Full Text (PDF, 0.5 MB)|
|Persistent link:|| http://urn.fi/urn:nbn:fi-fe2023081797492
|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.
|Pages:||527 - 542|
|Type of Publication:||
A1 Journal article – refereed
|Field of Science:||
Open Access funding provided by University of Oulu including Oulu University Hospital.
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