We provide the conditions under which a cellular automaton defined by certain classes of non-linear local rules exhibits surjectivity and reversibility. For the latter, the condition turns out to be a characterization. We also analyze the role of permutivity as a key factor influencing these properties and provide conditions that determine whether a non-linear CA in such classes is (bi)permutive.
Ben Ramdhane, F., Dennunzio, A., Margara, L., Menara, G. (2025). Structural Properties of Non-Linear Cellular Automata: Permutivity, Surjectivity, and Reversibility. In ICTCS 2025 Proceedings of the 26th Italian Conference on Theoretical Computer Science (pp.224-229). CEUR-WS.
Structural Properties of Non-Linear Cellular Automata: Permutivity, Surjectivity, and Reversibility
Ben Ramdhane F.;Dennunzio A.
;Menara G.
2025
Abstract
We provide the conditions under which a cellular automaton defined by certain classes of non-linear local rules exhibits surjectivity and reversibility. For the latter, the condition turns out to be a characterization. We also analyze the role of permutivity as a key factor influencing these properties and provide conditions that determine whether a non-linear CA in such classes is (bi)permutive.
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