We consider the family of all the Cellular Automata (CA) sharing the same local rule but have different memory, This family contains also all the CA with memory m ≤ 0 (one-sided CA) which can act both on Aℤ and on Aℕ. We study several set theoretical and topological properties for these classes. In particular we investigate if the properties of a given CA are preserved when we consider the CA obtained by changing the memory of the original one (shifting operation). Furthermore we focus our attention to the one-sided CA acting on Aℤ starting from the one-sided CA acting on Aℤ and having the same local rule (lifting operation). As a particular consequence of these investigations, we prove that the long-standing conjecture [Surjectivity ⇒ Density of the Periodic Orbits (DPO)] is equivalent to the conjecture [Topological Mixing ⇒ DPO. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Acerbi, L., Dennunzio, A., & Formenti, E. (2007). Shifting and lifting of cellular automata. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4497 LNCS, pp. 1–10). https://doi.org/10.1007/978-3-540-73001-9_1
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