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

Authors Julien Destombes, Andrei Romashchenko

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Author Details

Julien Destombes
  • LIRMM, University of Montpellier, Montpellier, France
Andrei Romashchenko
  • LIRMM, University of Montpellier, CNRS, Montpellier, France

Funding

projet ANR-15-CE40-0016 RaCAF

Acknowledgements

We are indebted to Bruno Durand, Alexander Shen, and Ilkka Törmä for fruitful discussions. We are grateful to Pierre Guillon and Emmanuel Jeandel for motivating comments. We also thank the anonymous referees of STACS 2019 for many valuable comments.

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Julien Destombes and Andrei Romashchenko. Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.STACS.2019.23

Abstract

We suggest 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 globally admissible patterns of size n x n grows only as a polynomial in n.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Information theory
  • Mathematics of computing → Combinatorics
Keywords
  • Sofic shifts
  • Block complexity
  • Kolmogorov complexity

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