On the Measure Entropy of Additive Cellular Automata f∞

@article{Akin2003OnTM,
  title={On the Measure Entropy of Additive Cellular Automata f∞},
  author={Hasan Akin},
  journal={Entropy},
  year={2003},
  volume={5},
  pages={233-238}
}
We show that for an additive one-dimensional cellular automata on space of all doubly infinitive sequences with values in a finite set S = {0, 1, 2, ..., r-1}, determined by an additive automaton rule f(x ∞ f n-k , ..., x n+k) = (mod r), and a-invariant uniform Bernoulli measure µ, the measure-theoretic entropy of the additive one-dimensional cellular automata with respect to µ is equal to h ∑ − = + k i k n x ∞ f k f ∞ f ∞ f µ () = 2klog r, where k ≥ 1, r-1∈S. We also show that the uniform… CONTINUE READING
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