Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Journal Articles Journal of Computer and System Sciences Year : 2022

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

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 globally admissible patterns of size $n\times n$ grows only as a polynomial in $n$. We also show that more conventional proofs of non-soficness for multi-dimensional effective shifts can be expressed interms of Kolmogorov complexity with unbounded computational resources. We also show that more conventional proofs of non-soficness for multi-dimensional effective shifts, including the techniques of Pavlov [Proc. AMS, 141(3):987-996, 2013] and Kass and Madden [Proc. AMS, 141(11):3803-3816, 2013], can be expressed in terms of Kolmogorov complexity with unbounded computational resources.
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Dates and versions

lirmm-03646717 , version 1 (11-10-2023)

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Julien Destombes, Andrei Romashchenko. Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts. Journal of Computer and System Sciences, 2022, 128, pp.107-134. ⟨10.1016/j.jcss.2022.04.002⟩. ⟨lirmm-03646717⟩
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