Structural Properties of Non-Linear Cellular Automata: Permutivity, Surjectivity and Reversibility
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912454181650432 |
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| author | Ramdhane, Firas Ben Dennunzio, Alberto Margara, Luciano Menara, Giuliamaria |
| author_facet | Ramdhane, Firas Ben Dennunzio, Alberto Margara, Luciano Menara, Giuliamaria |
| contents | This paper explores the algebraic conditions under which a cellular automaton with a non-linear local rule exhibits surjectivity and reversibility. We also analyze the role of permutivity as a key factor influencing these properties and provide conditions that determine whether a non-linear CA is (bi)permutive. Through theoretical results and illustrative examples, we characterize the relationships between these fundamental properties, offering new insights into the dynamical behavior of non-linear CA. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15949 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structural Properties of Non-Linear Cellular Automata: Permutivity, Surjectivity and Reversibility Ramdhane, Firas Ben Dennunzio, Alberto Margara, Luciano Menara, Giuliamaria Discrete Mathematics Cryptography and Security Dynamical Systems This paper explores the algebraic conditions under which a cellular automaton with a non-linear local rule exhibits surjectivity and reversibility. We also analyze the role of permutivity as a key factor influencing these properties and provide conditions that determine whether a non-linear CA is (bi)permutive. Through theoretical results and illustrative examples, we characterize the relationships between these fundamental properties, offering new insights into the dynamical behavior of non-linear CA. |
| title | Structural Properties of Non-Linear Cellular Automata: Permutivity, Surjectivity and Reversibility |
| topic | Discrete Mathematics Cryptography and Security Dynamical Systems |
| url | https://arxiv.org/abs/2504.15949 |