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NSRT diagram for identification of SACA and TACA rules in null-boundary

Author

Listed:
  • Mamata Dalui

    (Department of Computer Science and Engineering, National Institute of Technology Durgapur, West Bengal 713209, India)

  • Bidesh Chakraborty

    (��Department of Computer Science and Engineering, Haldia Institute of Technology, Haldia, West Bengal 721657, India)

  • Nilanjana Das

    (��Department of Computer Science and Technology, Indian Institute of Engineering Science and Technology, Shibpur, West Bengal 711103, India)

  • Biplab K. Sikdar

    (��Department of Computer Science and Technology, Indian Institute of Engineering Science and Technology, Shibpur, West Bengal 711103, India)

Abstract

This work reports characterization of one-dimensional null-boundary cellular automata (CA) rules in 3-neighborhood. The outcome of this characterization is the identification of CA rules that are the probable candidates for producing single length cycle attractor (fixed point). It targets synthesis of CA with only one fixed point (referred to as the single length cycle single attractor CA (SACA)) and the CA with only two fixed points (referred to as single length cycle two attractors CA (TACA)) for arbitrary length. A tool referred to as Next State RMT Transition Diagram (NSRTD) is developed to identify the fixed points as well as the cycles, involving multiple states (multi-length cycles) of a CA. The NSRTD provides the theoretical basis to search for the rules that form SACA and TACA, for all lengths, in null-boundary.

Suggested Citation

  • Mamata Dalui & Bidesh Chakraborty & Nilanjana Das & Biplab K. Sikdar, 2022. "NSRT diagram for identification of SACA and TACA rules in null-boundary," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 33(06), pages 1-25, June.
    • Handle: RePEc:wsi:ijmpcx:v:33:y:2022:i:06:n:s0129183122500711
    DOI: 10.1142/S0129183122500711
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