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Application of the graph cellular automaton in generating languages

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  • Praba, B.
  • Saranya, R.

Abstract

The purpose of this research is to strengthen the core of Cellular Automaton using the concept of Graph theory and Automata theory. In this paper we introduce a new approach of defining the Graph Cellular Automaton GCA, V,I,δ consisting of set of vertices and input symbols along with the time evolution function δ. Using the Basic Linear Rules, we define the kth generation GCA. This method enables us to capture the complete characterization of the future generations. When the defined GCA is taken as a graph corresponding to a given finite automaton, then the language generated by the kth generation GCA is predicted corresponding to the fundamental basic linear rules. This enables us to predict the language of the kth generation automaton using all the 512 rules. All explained concepts are illustrated with suitable examples.

Suggested Citation

  • Praba, B. & Saranya, R., 2020. "Application of the graph cellular automaton in generating languages," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 168(C), pages 111-121.
    • Handle: RePEc:eee:matcom:v:168:y:2020:i:c:p:111-121
    DOI: 10.1016/j.matcom.2019.07.010
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    References listed on IDEAS

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    1. Liu, Jia-Bao & Pan, Xiang-Feng, 2016. "Minimizing Kirchhoff index among graphs with a given vertex bipartiteness," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 84-88.
    2. Daniel Stevens & Suzana Dragićević, 2007. "A GIS-Based Irregular Cellular Automata Model of Land-Use Change," Environment and Planning B, , vol. 34(4), pages 708-724, August.
    3. Liu, Jia-Bao & Pan, Xiang-Feng & Hu, Fu-Tao & Hu, Feng-Feng, 2015. "Asymptotic Laplacian-energy-like invariant of lattices," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 205-214.
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