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Title: Characterization and Topological Behavior of Homomorphism Tree-Shifts
Authors: 班榮超
Ban, Jung-Chao
Chang, Chih-Hung
Hu, Wen-Guei
Lai, Guan-Yu
Contributors: 應數系
Keywords: Tree-SFT;Sofic tree-shift;Mixing property
Date: 2021-10
Issue Date: 2022-02-10 14:57:57 (UTC+8)
Abstract: The purpose of this article is twofold. On one hand, we reveal the equivalence of shift of finite type between a one-sided shift X and its associated hom tree-shift TX, as well as the equivalence in the sofic shift. On the other hand, we investigate the interrelationship among the comparable mixing properties on tree-shifts as those on multidimensional shift spaces. They include irreducibility, topologically mixing, block gluing, and strong irreducibility, all of which are defined in the spirit of classical multidimensional shift, complete prefix code (CPC), and uniform CPC. In summary, the mixing properties defined in all three manners coincide for TX. Furthermore, an equivalence between irreducibility on TA and irreducibility on XA are seen, and so is one between topologically mixing on TA and mixing property on XA, where XA is the one-sided shift space induced by the matrix A and TA is the associated tree-shift. These equivalences are consistent with the mixing properties on X or XA when viewed as a degenerate tree-shift.
Relation: Topology and its Applications, Volume 302, 107848
Data Type: article
DOI 連結:
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