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
Conference Papers Year : 2019

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

Abstract

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 $\mathbb{Z}^2$ with very low block complexity: the number of admissible patterns of size $n\times n$ grows only as a polynomial in $n$.
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lirmm-01793810 , version 1 (28-06-2019)

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Andrei Romashchenko, Julien Destombes. Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts. STACS 2019 - 36th International Symposium on Theoretical Aspects of Computer Science, Mar 2019, Berlin, Germany. pp.23:1--23:17, ⟨10.4230/LIPIcs.STACS.2019.23⟩. ⟨lirmm-01793810⟩
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