2025/04/22 by Ramdhane, Firas Ben, Dennunzio, Alberto, Margara, Luciano +1
#Cryptography and Security (cs.CR) #Discrete Mathematics (cs.DM) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2504.15949
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.