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The Algebraic Entropy of One-dimensional Finitary Linear Cellular Automata by Akın, Hasan; Dikranjan, Dikran; Bruno, Anna Giordano; Toller, Daniele is a scholarly article available to read on EtoBox.

What is The Algebraic Entropy of One-dimensional Finitary Linear Cellular Automata about?

The aim of this paper is to present one-dimensional finitary linear cellular automata $S$ on $\mathbb Z_m$ from an algebraic point of view. Among various other results, we: (i) show that the Pontryagin dual $\widehat S$ of $S$ is a classical one-dimensional linear cellular automaton $T$ on $\mathbb Z_m$; (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 $T=\widehat S$ by the so-called Bridge Theorem. In order to better understand and describe the entropy we introduce the degree $\mathrm{deg}(S)$ and $\mathrm{deg}(T)$ of $S$ and $T$.

Author

Akın, Hasan; Dikranjan, Dikran; Bruno, Anna Giordano; Toller, Daniele

Published

2023

Language

EN