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

05/10/2018

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by   Julien Destombes, et al.

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We propose necessary conditions of soficness of multidimensional shifts formulated in terms of resource-bounded Kolmogorov complexity. Using this technique we provide examples of effective and non-sofic shifts on Z^2 with very low block complexity: the number of admissible patterns of size n× n grows only as a polynomial in n.