A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Glider automata on all transitive sofic shifts
Tekijät: Kopra Johan
Kustantaja: Cambridge University Press
Julkaisuvuosi: 2022
Journal: Ergodic Theory and Dynamical Systems
Tietokannassa oleva lehden nimi: Ergodic Theory and Dynamical Systems
Vuosikerta: 42
Numero: 12
Aloitussivu: 3716
Lopetussivu: 3744
eISSN: 1469-4417
DOI: https://doi.org/10.1017/etds.2021.107
Verkko-osoite: https://doi.org/10.1017/etds.2021.107
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/67745009
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 This is an electronic reprint of the original article. |