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arXiv · 1603.00754

Matrix Characterization of Multidimensional Subshifts of Finite Type

Puneet Sharma·Dileep Kumar
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Abstract

Let $X\subset A^{Z^d}$ be a $2$-dimensional subshift of finite type. We prove that any $2$-dimensional multidimensional subshift of finite type can be characterized by a square matrix of infinite dimension. We extend our result to a general $d$-dimensional case. We prove that the multidimensional shift space is non-empty if and only if the matrix obtained is of positive dimension. In the process, we give an alternative view of the necessary and sufficient conditions obtained for the non-emptiness of the multidimensional shift space. We also give sufficient conditions for the shift space $X$ to exhibit periodic points.

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Puneet Sharma, Dileep Kumar. 2016-03-02. Matrix Characterization of Multidimensional Subshifts of Finite Type. https://arxiv.org/abs/1603.00754

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