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Glider Automorphisms on Some Shifts of Finite Type and a Finitary Ryan’s Theorem

  • Johan Kopra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10875)

Abstract

For any mixing SFT X containing a fixed point we construct a reversible shift-commuting continuous map (automorphism) which breaks any given finite point of the subshift into a finite collection of gliders traveling into opposing directions. As an application we show that the automorphism group \({{\mathrm{Aut}}}(X)\) contains a two-element subset S whose centralizer consists only of shift maps.

Keywords

Mixing SFTs Automorphisms Cellular automata 

Notes

Acknowledgments

The author thanks Ville Salo for helpful discussions concerning these topics.

References

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    Salo, V.: Transitive action on finite points of a full shift and a finitary Ryan’s theorem. arXiv:1610.05487v2 (2017)
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    Salo, V., Törmä, I.: A one-dimensional physically universal cellular automaton. In: Kari, J., Manea, F., Petre, I. (eds.) CiE 2017. LNCS, vol. 10307, pp. 375–386. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-58741-7_35CrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland

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