Corpus ID: 14299135

Decomposition of Additive CA

  title={Decomposition of Additive CA},
  author={Klaus Sutner},
We consider finite additive cellular automata with fixed and periodic boundary conditions as endomorphisms over pattern spaces. A characterization of the nilpotent and regular parts of these endomorphisms is given in terms of their minimal polynomials. We determine the generalized eigenspace decomposition, and describe relevant cyclic subspaces in terms of symmetries. As an application, we calculate the lengths and frequencies of limit cycles in the transition diagram of the automaton. 

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