A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Graph and wreath products of cellular automata
Tekijät: Salo, Ville
Kustantaja: WORLD SCIENTIFIC PUBL CO PTE LTD
Kustannuspaikka: SINGAPORE
Julkaisuvuosi: 2024
Lehti:: International Journal of Algebra and Computation
Tietokannassa oleva lehden nimi: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
Lehden akronyymi: INT J ALGEBR COMPUT
Sivujen määrä: 31
ISSN: 0218-1967
eISSN: 1793-6500
DOI: https://doi.org/10.1142/S0218196724500553
Verkko-osoite: https://doi.org/10.1142/S0218196724500553
Preprintin osoite: https://arxiv.org/abs/2012.10186
Tiivistelmä
We prove that the set of subgroups of the automorphism group of a two-sided full shift is closed under countable graph products. We introduce the notion of a group action without A-cancellation (for an abelian group A), and show that when A is a finite abelian group and G is a group of cellular automata whose action does not have A-cancellation, the wreath product A (sic) G embeds in the automorphism group of a full shift. We show that all free abelian groups and free groups admit such cellular automata actions. In the one-sided case, we prove variants of these results with reasonable alphabet blow-ups.
We prove that the set of subgroups of the automorphism group of a two-sided full shift is closed under countable graph products. We introduce the notion of a group action without A-cancellation (for an abelian group A), and show that when A is a finite abelian group and G is a group of cellular automata whose action does not have A-cancellation, the wreath product A (sic) G embeds in the automorphism group of a full shift. We show that all free abelian groups and free groups admit such cellular automata actions. In the one-sided case, we prove variants of these results with reasonable alphabet blow-ups.
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