Irreversibility of 2D Linear CA and Garden of Eden

Doston Jumaniyozov; Bakhrom Omirov; Shovkat Redjepov; Selman Uguz

doi:10.1142/S0218127423500657

Irreversibility of 2D Linear CA and Garden of Eden

Doston Jumaniyozov
, Bakhrom Omirov
, Shovkat Redjepov
, Selman Uguz

Academy of Sciences of the Republic of Uzbekistan
National University of Uzbekistan named after Mirzo Ulugbek
AKFA University
Tashkent University of Information Technologies named after Muhammad al-Khwarizmi
University of Texas at Dallas

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we consider a pentagonal lattice and we investigate the rule matrix with null boundary condition for two-dimensional cellular automata with the field Zp (the set of integers modulo Zp) and analyze their characteristics. Moreover, an algorithm of computing the rank of rule matrix with null boundary condition for von Neumann neighborhood is developed. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for two-dimensional cellular automata are obtained.

Original language	English
Article number	2350065
Journal	International Journal of Bifurcation and Chaos
Volume	33
Issue number	6
DOIs	https://doi.org/10.1142/S0218127423500657
State	Published - 1 May 2023
Externally published	Yes

Keywords

Cellular automata
Garden of Eden
neighborhood
pentagonal lattice
rule matrix

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10.1142/S0218127423500657

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abstract = "In this paper, we consider a pentagonal lattice and we investigate the rule matrix with null boundary condition for two-dimensional cellular automata with the field Zp (the set of integers modulo Zp) and analyze their characteristics. Moreover, an algorithm of computing the rank of rule matrix with null boundary condition for von Neumann neighborhood is developed. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for two-dimensional cellular automata are obtained.",

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AU - Jumaniyozov, Doston

AU - Omirov, Bakhrom

AU - Redjepov, Shovkat

AU - Uguz, Selman

PY - 2023/5/1

Y1 - 2023/5/1

N2 - In this paper, we consider a pentagonal lattice and we investigate the rule matrix with null boundary condition for two-dimensional cellular automata with the field Zp (the set of integers modulo Zp) and analyze their characteristics. Moreover, an algorithm of computing the rank of rule matrix with null boundary condition for von Neumann neighborhood is developed. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for two-dimensional cellular automata are obtained.

AB - In this paper, we consider a pentagonal lattice and we investigate the rule matrix with null boundary condition for two-dimensional cellular automata with the field Zp (the set of integers modulo Zp) and analyze their characteristics. Moreover, an algorithm of computing the rank of rule matrix with null boundary condition for von Neumann neighborhood is developed. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for two-dimensional cellular automata are obtained.

KW - Cellular automata

KW - Garden of Eden

KW - neighborhood

KW - pentagonal lattice

KW - rule matrix

UR - https://www.scopus.com/pages/publications/85161171626

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M3 - 文章

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JF - International Journal of Bifurcation and Chaos

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M1 - 2350065

ER -

Irreversibility of 2D Linear CA and Garden of Eden

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Keywords

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