Irreversibility of 2D Linear CA and Garden of Eden-Reference-Cited by-同舟云学术

Irreversibility of 2D Linear CA and Garden of Eden

Published:2023-05 Issue:06 Volume:33 Page:
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Jumaniyozov Doston¹^ORCID,Omirov Bakhrom²³,Redjepov Shovkat⁴,Uguz Selman⁵

Affiliation:

1. Romanovsky Institute of Mathematics of Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

2. National University of Uzbekistan, University Street 4, Tashkent 100174, Uzbekistan

3. Akfa University, Milliy Bog’ Street 264, Tashkent 111221, Uzbekistan

4. Tashkent University of Information Technologies, Tashkent, Uzbekistan

5. University of Texas at Dallas, Richardson, USA

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.

Funder

Ministry of Innovative Development of Uzbekistan

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127423500657

Reference23 articles.

1. Matrix algebraic formulae concerning some exceptional rules of two-dimensional cellular automata

2. Inversion of 2D cellular automata: some complexity results

3. Endomorphisms and automorphisms of the shift dynamical system