A Characterization of Cellular Automata Generated by Idempotents on the Full Shift

  • Ville Salo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7353)

Abstract

In this article, we discuss the family of cellular automata generated by so-called idempotent cellular automata (CA G such that G 2 = G) on the full shift. We prove a characterization of products of idempotent CA, and show examples of CA which are not easy to directly decompose into a product of idempotents, but which are trivially seen to satisfy the conditions of the characterization. Our proof uses ideas similar to those used in the well-known Embedding Theorem and Lower Entropy Factor Theorem in symbolic dynamics. We also consider some natural decidability questions for the class of products of idempotent CA.

Keywords

Cellular Automaton Periodic Point Symbolic Dynamic Spreading State Decidability Question 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ville Salo
    • 1
  1. 1.University of TurkuFinland

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