Structural Properties of Non-Linear Cellular Automata: Permutivity, Surjectivity and Reversibility
By: Firas Ben Ramdhane , Alberto Dennunzio , Luciano Margara and more
Potential Business Impact:
Makes computer rules predictable and reversible.
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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