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Solutions to All-Colors Problem on Graph Cellular Automata

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  • Xiaoyan Zhang
  • Chao Wang

Abstract

The All-Ones Problem comes from the theory of - 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, - Random Weak-All-Colors Problem, which is relevant to both combinatorial number theory and cellular automata theory.

Suggested Citation

  • Xiaoyan Zhang & Chao Wang, 2019. "Solutions to All-Colors Problem on Graph Cellular Automata," Complexity, Hindawi, vol. 2019, pages 1-11, June.
    • Handle: RePEc:hin:complx:3164692
    DOI: 10.1155/2019/3164692
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    References listed on IDEAS

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    1. Barrett, Chris L & Chen, William Y.C & Zheng, Michelle J, 2004. "Discrete dynamical systems on graphs and Boolean functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(6), pages 487-497.
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