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<dc:title>2D linear CA with mixing boundary conditions and reversibility</dc:title>
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<dc:creator>Casas Mirás, José Manuel</dc:creator>
<dc:creator>Ladra González, Manuel</dc:creator>
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<dcterms:abstract>In this paper, we consider two-dimensional cellular automata (CA) with the von Neumann neighborhood. We study the characterization of 2D linear cellular automata defined by the von Neumann neighborhood with new type of boundary conditions over the field Zp. Furthermore, we investigate the rule matrices of 2D von Neumann CA by applying the group of permutations S4. Moreover, the algorithm for computing the rank of rule matrices is given. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for considered two-dimensional cellular automata are obtained.</dcterms:abstract>
<dcterms:issued>2023-06-30</dcterms:issued>
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<dc:title>2D linear CA with mixing boundary conditions and reversibility</dc:title>
<dc:creator>Jumaniyozov, Doston</dc:creator>
<dc:creator>Casas Mirás, José Manuel</dc:creator>
<dc:creator>Ladra González, Manuel</dc:creator>
<dc:creator>Omirov, Bakhrom</dc:creator>
<dc:creator>Redjepov, Shovkat</dc:creator>
<dc:description>In this paper, we consider two-dimensional cellular automata (CA) with the von Neumann neighborhood. We study the characterization of 2D linear cellular automata defined by the von Neumann neighborhood with new type of boundary conditions over the field Zp. Furthermore, we investigate the rule matrices of 2D von Neumann CA by applying the group of permutations S4. Moreover, the algorithm for computing the rank of rule matrices is given. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for considered two-dimensional cellular automata are obtained.</dc:description>
<dc:date>2023-12-05T11:18:37Z</dc:date>
<dc:date>2023-06-30</dc:date>
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<dcterms:abstract lang="en">In this paper, we consider two-dimensional cellular automata (CA) with the von Neumann neighborhood. We study the characterization of 2D linear cellular automata defined by the von Neumann neighborhood with new type of boundary conditions over the field Zp. Furthermore, we investigate the rule matrices of 2D von Neumann CA by applying the group of permutations S4. Moreover, the algorithm for computing the rank of rule matrices is given. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for considered two-dimensional cellular automata are obtained.</dcterms:abstract>
<dcterms:description_sponsorship lang="spa">Agencia Estatal de Investigación | Ref. PID2020-115155GB-I00</dcterms:description_sponsorship>
<dcterms:description_sponsorship lang="spa">Ministry of Innovative Development of Uzbekistan | Ref. FZ-20200930492</dcterms:description_sponsorship>
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<dcterms:title lang="en">2D linear CA with mixing boundary conditions and reversibility</dcterms:title>
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<dcterms:subject lang="spa">1201.11 Teoría de Matrices</dcterms:subject>
<dcterms:authorList>Jumaniyozov, Doston#105#Ladra González, Manuel#Omirov, Bakhrom#Redjepov, Shovkat</dcterms:authorList>
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