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arXiv · 1805.03929

Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts

Julien Destombes·Andrei Romashchenko
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Abstract

We suggest necessary conditions of soficness of multidimensional shifts formulated in termsof resource-bounded Kolmogorov complexity. Using this technique we provide examples ofeffective and non-sofic shifts on $\mathbb{Z}^2$ with very low block complexity: the number of globallyadmissible patterns of size $n\times n$ grows only as a polynomial in $n$. We also show that moreconventional proofs of non-soficness for multi-dimensional effective shifts can be expressed interms of Kolmogorov complexity with unbounded computational resources.

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Julien Destombes, Andrei Romashchenko. 2018-05-10. Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts. https://doi.org/10.1016/j.jcss.2022.04.002

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