Decidability of Irreducible Tree Shifts of Finite Type

Ban, Jung-Chao; Chang, Chih-Hung; Huang, Nian-Ning; Wu, Yu-Liang

doi:10.1007/s10955-019-02407-z

Cited by 4 publications

(1 citation statement)

References 35 publications

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“…For instance, the topological conjugacy between two superior symbolic systems (shifts of finite type, to be precise) is decidable; irreducible shifts of finite type are chaotic in Devaney's sense; a stronger type of irreducibility is decidable. See [1,2,3,4,5,9,16] and the references therein for more details.…”

Section: Introductionmentioning

confidence: 99%

Stem and topological entropy on Cayley trees

Ban,

Chang,

et al. 2021

Preprint

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We consider the existence of the topological entropy of shift spaces on a finitely generated semigroup whose Cayley graph is a tree. The considered semigroups include free groups. On the other hand, the notion of stem entropy is introduced. For shift spaces on a strict free semigroup, the stem entropy coincides with the topological entropy. We reveal a sufficient condition for the existence of the stem entropy of shift spaces on a semigroup. Furthermore, we demonstrate that the topological entropy exists in many cases and is identical to the stem entropy.

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Section: Introductionmentioning

confidence: 99%

Stem and topological entropy on Cayley trees

Ban,

Chang,

et al. 2021

Preprint

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Decidability of CPC-irreducibility of subshifts of finite type over free groups

Ban

Chang

2023

Semigroup Forum

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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 $$({\textsf{d}},{\textsf{c}})$$ ( 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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Stem and topological entropy on Cayley trees

Ban

Chang

et al. 2021

Math Phys Anal Geom

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Decidability of Irreducible Tree Shifts of Finite Type

Cited by 4 publications

References 35 publications

Stem and topological entropy on Cayley trees

Stem and topological entropy on Cayley trees

Decidability of CPC-irreducibility of subshifts of finite type over free groups

Stem and topological entropy on Cayley trees

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