Abstract
Two cellular automata (CAs) are said to be isomorphic if their respective configuration transition diagrams are isomorphic. In this paper, we propose two schemes to determine the set of CAs that are isomorphic to any given cellular automaton (CA). Our first procedure works by permutation of the states of a set of cell positions of the CA. This methodology can be applied to generate at most \((d!)^n -1\) isomorphic cellular automata each of which will maintain the same neighborhood as the given n-cell d-state CA. Whereas, our second procedure does an exchange of the cells at different positions; we show that the isomorphic cellular automata generated in this manner may have larger neighborhood than the input CA, depending on the range of cell positions exchanged. An extensive experimentation has been done to establish the efficacy of our schemes.
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Acknowledgements
This work is partially supported by Start-up Research Grant (File number SRG/2022/002098), SERB, Department of Science & Technology, Government of India. It is partially done as a project in Indian Summer School on Cellular Automata 2022. The authors are grateful to Prof. Sukanta Das for his valuable comments and suggestions and Mr. Tushar Bhatt for his help in the implementation of the schemes.
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Mukherjee, S., Vikrant, V., Bhattacharjee, K. (2023). Isomorphism in Cellular Automata. In: Das, S., Martinez, G.J. (eds) Proceedings of Second Asian Symposium on Cellular Automata Technology. ASCAT 2023. Advances in Intelligent Systems and Computing, vol 1443. Springer, Singapore. https://doi.org/10.1007/978-981-99-0688-8_15
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DOI: https://doi.org/10.1007/978-981-99-0688-8_15
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