Abstract
We consider the family of all the Cellular Automata (CA) sharing the same local rule but having different memories. This family contains also all CA with memory m ≤ 0 (one-sided CA) which can act both on A Z and on A N . We study several set theoretical and topological properties for these classes. In particular, we investigate whether the properties of a given CA are preserved when considering the CA obtained by changing the memory of the original one (shifting operation). Furthermore, we focus our attention on the one-sided CA acting on A Z , starting from the one-sided CA acting on A N and having the same local rule (lifting operation). As a particular consequence of these investigations, we prove that the long-standing conjecture [Surjectivity ⇒ Dense Periodic Orbits (DPO)] can be restated in several different (but equivalent) ways. Furthermore, we give some results on properties conserved under the iteration of the CA global map.
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