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Glider automata on all transitive sofic shifts




TekijätKopra Johan

KustantajaCambridge University Press

Julkaisuvuosi2022

JournalErgodic Theory and Dynamical Systems

Tietokannassa oleva lehden nimiErgodic Theory and Dynamical Systems

Vuosikerta42

Numero12

Aloitussivu3716

Lopetussivu3744

eISSN1469-4417

DOIhttps://doi.org/10.1017/etds.2021.107

Verkko-osoitehttps://doi.org/10.1017/etds.2021.107

Rinnakkaistallenteen osoitehttps://research.utu.fi/converis/portal/detail/Publication/67745009


Tiivistelmä

For any infinite transitive sofic shift X we construct a reversible cellular automaton (that is, an automorphism of the shift X) which breaks any given finite point of the subshift into a finite collection of gliders traveling into opposing directions. This shows in addition that every infinite transitive sofic shift has a reversible cellular automaton which is sensitive with respect to all directions. As another application we prove a finitary version of Ryan’s theorem: the automorphism group Aut(X) contains a two-element subset whose centralizer consists only of shift maps. We also show that in the class of S-gap shifts these results do not extend beyond the sofic case.


Ladattava julkaisu

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Last updated on 2024-26-11 at 21:36