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

Research output: Contribution to journal › Article › 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.

Original language	English
Pages (from-to)	157-177
Number of pages	21
Journal	Theoretical Computer Science
Volume	221
Issue number	1-2
DOIs	https://doi.org/10.1016/S0304-3975(99)00031-6
Publication status	Published - 28 Jun 1999
Externally published	Yes

Keywords

Discrete time dynamical systems
Linear cellular automata
Topological properties

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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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author = "Giovanni Manzini and Luciano Margara",

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AU - Manzini, Giovanni

AU - Margara, Luciano

PY - 1999/6/28

Y1 - 1999/6/28

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

UR - https://www.scopus.com/pages/publications/0004598616

U2 - 10.1016/S0304-3975(99)00031-6

DO - 10.1016/S0304-3975(99)00031-6

M3 - Article

SN - 0304-3975

VL - 221

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EP - 177

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 1-2

ER -

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

Abstract

Keywords

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