Pseudo-cyclic renewal systems |
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Authors: | Sujin Shin |
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Affiliation: | Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea |
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Abstract: | A finite set W of words over an alphabet A is cyclic if, whenever u,v∈A∗ and uv,vu∈W∗, we have u,v∈W∗. If it is only assumed that the property holds for all u,v∈A∗ with a large length, then W is called pseudo-cyclic, that is, there is N∈N such that, whenever u,v∈A∗ with |u|, |v|≥N and uv,vu∈W∗, we have u,v∈W∗. We analyze the class of pseudo-cyclic sets and describe how it is related to the open question which asks whether every irreducible shift of finite type is conjugate to a renewal system. |
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Keywords: | Cyclic Pseudo-cyclic Semi-cyclic Bifix-free Fiber mixing Circular mixing |
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