Substitution Point of View
Let σ be a q-uniform morphism of the free monoid E∗, so that and which is prolongable on : that is, σ(e) begins with e. Let also be A and π as before. Then if w is a fixpoint of σ, that is to say w = σ(w), then m = π(w) is a q-automatic sequence over A: this is Cobham's theorem. Conversely every q-automatic sequence is obtained in this way.
Read more about this topic: Automatic Sequence
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