TY - JOUR
T1 - The algebraic entropy of one-dimensional finitary linear cellular automata
AU - Toller, Daniele
AU - Dikranjan, Dikran
AU - Giordano Bruno, Anna
AU - Akin, Hasan
PY - 2024
Y1 - 2024
N2 - The aim of this paper is to present one-dimensional finitary linear cellular automata S on Zm from an algebraic point of view. Among various other results, we (i) show that the Pontryagin dual SO of S is a classical one-dimensional linear cellular automaton T on Zm; (ii) give several equivalent conditions for S to be invertible with inverse a finitary linear cellular automaton; (iii) compute the algebraic entropy of S, which coincides with the topological entropy of T D SO by the so-called Bridge Theorem. In order to better understand and describe entropy, we introduce the degree deg.S/ and deg.T / of S and T .
AB - The aim of this paper is to present one-dimensional finitary linear cellular automata S on Zm from an algebraic point of view. Among various other results, we (i) show that the Pontryagin dual SO of S is a classical one-dimensional linear cellular automaton T on Zm; (ii) give several equivalent conditions for S to be invertible with inverse a finitary linear cellular automaton; (iii) compute the algebraic entropy of S, which coincides with the topological entropy of T D SO by the so-called Bridge Theorem. In order to better understand and describe entropy, we introduce the degree deg.S/ and deg.T / of S and T .
UR - http://www.scopus.com/inward/record.url?scp=85184914921&partnerID=8YFLogxK
U2 - 10.1515/jgth-2023-0092
DO - 10.1515/jgth-2023-0092
M3 - Journal article
SN - 1435-4446
JO - Journal of Group Theory
JF - Journal of Group Theory
ER -