Welch sets for random generation and representation of reversible one-dimensional cellular automata

被引：4

作者：

Carlos Seck-Tuoh-Mora, Juan ^{[1
]}

Medina-Marin, Joselito ^{[1
]}

Hernandez-Romero, Norberto ^{[1
]}

Martinez, Genaro J. ^{[2
,3
]}

Barragan-Vite, Irving ^{[1
]}

机构：

[1] AAI ICBI UAEH, Carr Pachuca Tulancingo Km 4-5, Pachuca 42184, Hidalgo, Mexico

[2] Univ West England, Unconvent Comp Ctr, Bristol BS16 1QY, Avon, England

[3] Inst Politecn Nacl, Escuela Super Computo, Mexico City 07738, DF, Mexico

来源：

INFORMATION SCIENCES | 2017年 / 382卷

关键词：

Cellular automata; Reversibility; Welch indices; Bipartite graph; Block mapping; ALGORITHM; GROUPOIDS; MEMORY;

D O I：

10.1016/j.ins.2016.12.009

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Reversible one-dimensional cellular automata are studied from the perspective of Welch Sets. This paper presents an algorithm to generate random Welch sets that define a reversible cellular automaton. Then, properties of Welch sets are used in order to establish two bipartite graphs describing the evolution rule of reversible cellular automata. The first graph gives an alternative representation for the dynamics of these systems as block mappings and shifts. The second graph offers a compact representation for the evolution rule of reversible cellular automata. Both graphs and their matrix representations are illustrated by the generation of random reversible cellular automata with 6 and 18 states. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：81 / 95

页数：15

共 50 条

[1] Transitive behavior in reversible one-dimensional cellular automata with a Welch index 1
Mora, JCST
[J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2002, 13 (06): : 837 - 855
[2] Reversible one-dimensional cellular automata with one of the two Welch indices equal to 1 and full shifts
Mora, JCSL
Hernández, MG
Vergara, SVC
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (29): : 7989 - 8001
[3] THE STRUCTURE OF REVERSIBLE ONE-DIMENSIONAL CELLULAR AUTOMATA
HILLMAN, D
[J]. PHYSICA D, 1991, 52 (2-3): : 277 - 292
[4] One-dimensional pattern generation by cellular automata
Kutrib, Martin
Malcher, Andreas
[J]. NATURAL COMPUTING, 2022, 21 (03) : 361 - 375
[5] Simple universal one-dimensional reversible cellular automata
Morita, Kenichi
[J]. JOURNAL OF CELLULAR AUTOMATA, 2007, 2 (02) : 159 - 165
[6] One-dimensional pattern generation by cellular automata
Martin Kutrib
Andreas Malcher
[J]. Natural Computing, 2022, 21 : 361 - 375
[7] Spectral properties of reversible one-dimensional cellular automata
Mora, JCST
Vergara, SVC
Martinez, GJ
McIntosh, HV
[J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2003, 14 (03): : 379 - 395
[8] One-Dimensional Pattern Generation by Cellular Automata
Kutrib, Martin
Malcher, Andreas
[J]. CELLULAR AUTOMATA, ACRI 2020, 2021, 12599 : 46 - 55
[9] Procedures for calculating reversible one-dimensional cellular automata
Mora, JCST
Vergara, SVC
Martínez, GJ
McIntosh, HV
[J]. PHYSICA D-NONLINEAR PHENOMENA, 2005, 202 (1-2) : 134 - 141
[10] Hybrid one-dimensional reversible cellular automata are regular
Bingham, Jesse
Bingham, Brad
[J]. DISCRETE APPLIED MATHEMATICS, 2007, 155 (18) : 2555 - 2566

← 1 2 3 4 5 →