Article

Irreversibility of 2D Linear CA and Garden of Eden

Doston JumaniyozovRomanovsky Institute of Mathematics of Uzbekistan Academy of Sciences, Tashkent, UzbekistanB. A. OmirovAkfa University, Milliy Bog’ Street 264, Tashkent 111221, UzbekistanShovkat RedjepovTashkent University of Information Technologies, Tashkent, UzbekistanSelman UǧuzUniversity of Texas at Dallas, Richardson, USA

International Journal of Bifurcation and Chaosjournal2023en

ABI

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 [Formula: see text] (the set of integers modulo [Formula: see text]) 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.

Topics

Cellular Automata and Applications DNA and Biological Computing Computability, Logic, AI Algorithms

Identifiers

DOI: 10.1142/s0218127423500657

Citations and references

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