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Journal article
An efficiently computable characterization of stability and instability for linear cellular automata
Journal of computer and system sciences, v 122, pp 63-71
Dec 2021
Abstract
We provide an efficiently computable characterization of two important properties describing stable and unstable complex behaviours as equicontinuity and sensitivity to the initial conditions for one-dimensional linear cellular automata (LCA) over (Z/mZ)n. We stress that the setting of LCA over (Z/mZ)n with n>1 is more expressive, it gives rise to much more complex dynamics, and it is more difficult to deal with than the already investigated case n=1. Indeed, in order to get our result we need to prove a nontrivial result of abstract algebra: if K is any finite commutative ring and L is any K-algebra, then for every pair A, B of n×n matrices over L having the same characteristic polynomial, it holds that the set {A0,A1,A2,…} is finite if and only if the set {B0,B1,B2,…} is finite too.
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Details
- Title
- An efficiently computable characterization of stability and instability for linear cellular automata
- Creators
- Alberto Dennunzio - University of Milano-BicoccaEnrico Formenti - Observatoire de la Côte d’AzurDarij Grinberg - Mathematical Research Institute of OberwolfachLuciano Margara - University of Bologna
- Publication Details
- Journal of computer and system sciences, v 122, pp 63-71
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000685466000004
- Scopus ID
- 2-s2.0-85119628355
- Other Identifier
- 991021862236804721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Computer Science, Hardware & Architecture
- Computer Science, Theory & Methods