A complete and efficiently computable topological classification of D-dimensional linear cellular automata over Zm

Giovanni Manzini; Luciano Margara

doi:10.1016/S0304-3975(99)00031-6

A complete and efficiently computable topological classification of D-dimensional linear cellular automata over Z_m

Giovanni Manzini, Luciano Margara

Risultato della ricerca: Contributo su rivista › Articolo in rivista › peer review

Abstract

We study the dynamical behavior of D-dimensional linear cellular automata over Z_m. We provide easy-to-check necessary and sufficient conditions for a D-dimensional linear cellular auwbdifq03 tomata over Z_m to be sensitive to initial conditions, positively expansive, strongly transitive, and equicontinuous. As a consequence of our results, we have a complete and efficiently computable topological classification of D-dimensional linear cellular automata over Z_m according to the most important dynamical properties studied in the theory of discrete time dynamical systems.

Lingua originale	Inglese
pagine (da-a)	157-177
Numero di pagine	21
Rivista	Theoretical Computer Science
Volume	221
Numero di pubblicazione	1-2
DOI	https://doi.org/10.1016/S0304-3975(99)00031-6
Stato di pubblicazione	Pubblicato - 28 giu 1999
Pubblicato esternamente	Sì

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10.1016/S0304-3975(99)00031-6

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abstract = "We study the dynamical behavior of D-dimensional linear cellular automata over Zm. We provide easy-to-check necessary and sufficient conditions for a D-dimensional linear cellular auwbdifq03 tomata over Zm to be sensitive to initial conditions, positively expansive, strongly transitive, and equicontinuous. As a consequence of our results, we have a complete and efficiently computable topological classification of D-dimensional linear cellular automata over Zm according to the most important dynamical properties studied in the theory of discrete time dynamical systems.",

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AU - Margara, Luciano

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N2 - We study the dynamical behavior of D-dimensional linear cellular automata over Zm. We provide easy-to-check necessary and sufficient conditions for a D-dimensional linear cellular auwbdifq03 tomata over Zm to be sensitive to initial conditions, positively expansive, strongly transitive, and equicontinuous. As a consequence of our results, we have a complete and efficiently computable topological classification of D-dimensional linear cellular automata over Zm according to the most important dynamical properties studied in the theory of discrete time dynamical systems.

AB - We study the dynamical behavior of D-dimensional linear cellular automata over Zm. We provide easy-to-check necessary and sufficient conditions for a D-dimensional linear cellular auwbdifq03 tomata over Zm to be sensitive to initial conditions, positively expansive, strongly transitive, and equicontinuous. As a consequence of our results, we have a complete and efficiently computable topological classification of D-dimensional linear cellular automata over Zm according to the most important dynamical properties studied in the theory of discrete time dynamical systems.

KW - Discrete time dynamical systems

KW - Linear cellular automata

KW - Topological properties

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