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Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts (1805.03929v9)
Published 10 May 2018 in cs.DM and cs.CC
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.