The Invertibility of Cellular Automata with Menory: Correcting Errors and New Conclusions
<|reference_start|>The Invertibility of Cellular Automata with Menory: Correcting Errors and New Conclusions: Cellular automata with memory (CAM) are widely used in fields such as image processing, pattern recognition, simulation, and cryptography. The invertibility of CAM is generally considered to be chaotic. Paper [Invertible behavior in elementary cellular automata with memory, Juan C. Seck-Tuoh-Mora et al., Information Sciences, 2012] presented necessary and sufficient conditions for the invertibility of elementary CAM, but it contains a critical error: it classifies identity CAM as non-invertible, whereas identity CAM is undoubtedly invertible. By integrating Amoroso's algorithm and cycle graphs, we provide the correct necessary and sufficient conditions for the invertibility of one-dimensional CAM. Additionally, we link CAM to a specific type of cellular automaton that is isomorphic to CAM, behaves identically, and has easily determinable invertibility. This makes it a promising alternative tool for CAM applications.<|reference_end|>
@article{wang2024the,
    title={The Invertibility of Cellular Automata with Menory: Correcting Errors
  and New Conclusions},
    author={Chen Wang, Xiang Deng and Chao Wang},
    journal={arXiv preprint arXiv:2406.05642},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.05642},
    primaryClass={nlin.CG cs.DS}
}