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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Shifting and Lifting of Cellular Automata
verfasst von : Luigi Acerbi, Alberto Dennunzio, Enrico Formenti
Erschienen in: Computation and Logic in the Real World
Verlag: Springer Berlin Heidelberg
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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
A
ℤ
and on
A
ℕ
. 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
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
$\Rightarrow$
Density of the Periodic Orbits (DPO)] is equivalent to the conjecture [Topological Mixing
$\Rightarrow$
DPO].