Solutions to All-Colors Problem on Graph Cellular Automata

Solutions to All-Colors Problem on Graph Cellular Automata

The All-Ones Problem comes from the theory of σ+-automata, which is related to graph dynamical systems as well as the Odd Set Problem in linear decoding. In this paper, we further study and compute the solutions to the “All-Colors Problem,” a generalization of “All-Ones Problem,” on some interesting...

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Main Authors: Xiaoyan Zhang, Chao Wang
Format: Article
Language:English
Published: Hindawi-Wiley 2019-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2019/3164692
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spelling doaj-36c15e3d7ce240448412a16041d6c8c92020-11-25T01:05:18ZengHindawi-WileyComplexity1076-27871099-05262019-01-01201910.1155/2019/31646923164692Solutions to All-Colors Problem on Graph Cellular AutomataXiaoyan Zhang0Chao Wang1School of Mathematical Science & Institute of Mathematics, Nanjing Normal University, Jiangsu 210023, ChinaCollege of Software, Nankai University, Tianjin 300350, ChinaThe All-Ones Problem comes from the theory of σ+-automata, which is related to graph dynamical systems as well as the Odd Set Problem in linear decoding. In this paper, we further study and compute the solutions to the “All-Colors Problem,” a generalization of “All-Ones Problem,” on some interesting classes of graphs which can be divided into two subproblems: Strong-All-Colors Problem and Weak-All-Colors Problem, respectively. We also introduce a new kind of All-Colors Problem, k-Random Weak-All-Colors Problem, which is relevant to both combinatorial number theory and cellular automata theory.http://dx.doi.org/10.1155/2019/3164692
collection DOAJ
language English
format Article
sources DOAJ
author Xiaoyan Zhang
Chao Wang
spellingShingle Xiaoyan Zhang
Chao Wang
Solutions to All-Colors Problem on Graph Cellular Automata
Complexity
author_facet Xiaoyan Zhang
Chao Wang
author_sort Xiaoyan Zhang
title Solutions to All-Colors Problem on Graph Cellular Automata
title_short Solutions to All-Colors Problem on Graph Cellular Automata
title_full Solutions to All-Colors Problem on Graph Cellular Automata
title_fullStr Solutions to All-Colors Problem on Graph Cellular Automata
title_full_unstemmed Solutions to All-Colors Problem on Graph Cellular Automata
title_sort solutions to all-colors problem on graph cellular automata
publisher Hindawi-Wiley
series Complexity
issn 1076-2787
1099-0526
publishDate 2019-01-01
description The All-Ones Problem comes from the theory of σ+-automata, which is related to graph dynamical systems as well as the Odd Set Problem in linear decoding. In this paper, we further study and compute the solutions to the “All-Colors Problem,” a generalization of “All-Ones Problem,” on some interesting classes of graphs which can be divided into two subproblems: Strong-All-Colors Problem and Weak-All-Colors Problem, respectively. We also introduce a new kind of All-Colors Problem, k-Random Weak-All-Colors Problem, which is relevant to both combinatorial number theory and cellular automata theory.
url http://dx.doi.org/10.1155/2019/3164692
work_keys_str_mv AT xiaoyanzhang solutionstoallcolorsproblemongraphcellularautomata
AT chaowang solutionstoallcolorsproblemongraphcellularautomata
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