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Identification of ECA rules forming MACA in periodic boundary condition

Author

Listed:
  • Som Banerjee

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

  • Mamata Dalui

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

Abstract

Cellular automaton (CA) is a computing model which is emerging rapidly. It is largely used in different types of scientific applications and simulations due to its ability to solve complex problems using simple rule(s). Cellular automata (CAs) are used in different types of applications like cryptography, VLSI systems, fault detection, etc. Typically, most of these applications utilize one-dimensional, 2-state, 3-neighborhood CAs. This paper explores the concept of Next State RMT Transition Diagram (NSRTD) for characterization of all the Elementary Cellular Automata (ECA) rules in periodic boundary condition leading to the identification of all ECA rules forming more than two fixed points (referred to as Single Length Cycle Multi-Attractor CA (MACA)) for an arbitrary CA length (n). For this, the 88 Wolfram classification rules and their equivalent rules have been utilized to reduce the search complexity by avoiding exhaustive searching on all the 256 ECA rules.

Suggested Citation

  • Som Banerjee & Mamata Dalui, 2025. "Identification of ECA rules forming MACA in periodic boundary condition," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-17, January.
    • Handle: RePEc:wsi:ijmpcx:v:36:y:2025:i:01:n:s0129183124501730
    DOI: 10.1142/S0129183124501730
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