Shifting and Lifting of Cellular Automata

  • Luigi Acerbi
  • Alberto Dennunzio
  • Enrico Formenti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4497)

Abstract

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 and on A. 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 starting from the one-sided CA acting on A 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].

Keywords

discrete time dynamical systems cellular automata topological dynamics deterministic chaos 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Luigi Acerbi
    • 1
  • Alberto Dennunzio
    • 1
  • Enrico Formenti
    • 2
  1. 1.Università degli Studi di Milano–Bicocca, Dipartimento di Informatica, Sistemistica e Comunicazione, Via Bicocca degli Arcimboldi 8, 20126 MilanoItaly
  2. 2.Université de Nice-Sophia Antipolis, Laboratoire I3S, 2000 Route des Colles, 06903 Sophia AntipolisFrance

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