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arXiv · 2504.15949

Structural Properties of Non-Linear Cellular Automata: Permutivity, Surjectivity and Reversibility

Firas Ben Ramdhane·Alberto Dennunzio·Luciano Margara·Giuliamaria Menara
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Abstract

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.

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Firas Ben Ramdhane, Alberto Dennunzio, Luciano Margara, Giuliamaria Menara. 2025-04-22. Structural Properties of Non-Linear Cellular Automata: Permutivity, Surjectivity and Reversibility. https://arxiv.org/abs/2504.15949

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