Reversibility of Symmetric Linear Cellular Automata with Radius <i>r</i> = 3

Reversibility of Symmetric Linear Cellular Automata with Radius <i>r</i> = 3

The aim of this work is to completely solve the reversibility problem for symmetric linear cellular automata with radius <inline-formula> <math display="inline"> <semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>3</mn> </mrow> &l...

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Main Authors: A. Martín del Rey, R. Casado Vara, D. Hernández Serrano
Format: Article
Language:English
Published: MDPI AG 2019-09-01
Series:Mathematics
Subjects:
linear cellular automata
reversibility
symmetric rules
Online Access:https://www.mdpi.com/2227-7390/7/9/816
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spelling doaj-547a47295c8741509d2f349299d45d4e2020-11-25T01:09:43ZengMDPI AGMathematics2227-73902019-09-017981610.3390/math7090816math7090816Reversibility of Symmetric Linear Cellular Automata with Radius <i>r</i> = 3A. Martín del Rey0R. Casado Vara1D. Hernández Serrano2Department of Applied Mathematics, IUFFyM, University of Salamanca, 37008-Salamanca, SpainBISITE Research Group, University of Salamanca, 37008-Salamanca, SpainDepartment of Mathematics, IUFFyM, University of Salamanca, 37008-Salamanca, SpainThe aim of this work is to completely solve the reversibility problem for symmetric linear cellular automata with radius <inline-formula> <math display="inline"> <semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics> </math> </inline-formula> and null boundary conditions. The main result obtained is the explicit computation of the local transition functions of the inverse cellular automata. This allows introduction of possible and interesting applications in digital image encryption.https://www.mdpi.com/2227-7390/7/9/816linear cellular automatareversibilitysymmetric rules
collection DOAJ
language English
format Article
sources DOAJ
author A. Martín del Rey
R. Casado Vara
D. Hernández Serrano
spellingShingle A. Martín del Rey
R. Casado Vara
D. Hernández Serrano
Reversibility of Symmetric Linear Cellular Automata with Radius <i>r</i> = 3
Mathematics
linear cellular automata
reversibility
symmetric rules
author_facet A. Martín del Rey
R. Casado Vara
D. Hernández Serrano
author_sort A. Martín del Rey
title Reversibility of Symmetric Linear Cellular Automata with Radius <i>r</i> = 3
title_short Reversibility of Symmetric Linear Cellular Automata with Radius <i>r</i> = 3
title_full Reversibility of Symmetric Linear Cellular Automata with Radius <i>r</i> = 3
title_fullStr Reversibility of Symmetric Linear Cellular Automata with Radius <i>r</i> = 3
title_full_unstemmed Reversibility of Symmetric Linear Cellular Automata with Radius <i>r</i> = 3
title_sort reversibility of symmetric linear cellular automata with radius <i>r</i> = 3
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-09-01
description The aim of this work is to completely solve the reversibility problem for symmetric linear cellular automata with radius <inline-formula> <math display="inline"> <semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics> </math> </inline-formula> and null boundary conditions. The main result obtained is the explicit computation of the local transition functions of the inverse cellular automata. This allows introduction of possible and interesting applications in digital image encryption.
topic linear cellular automata
reversibility
symmetric rules
url https://www.mdpi.com/2227-7390/7/9/816
work_keys_str_mv AT amartindelrey reversibilityofsymmetriclinearcellularautomatawithradiusiri3
AT rcasadovara reversibilityofsymmetriclinearcellularautomatawithradiusiri3
AT dhernandezserrano reversibilityofsymmetriclinearcellularautomatawithradiusiri3
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