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
Famous quotes containing the words point of view, substitution, point and/or view:
“All our Concord waters have two colors at least; one when viewed at a distance, and another, more proper, close at hand.... Walden is blue at one time and green at another, even from the same point of view. Lying between the earth and the heavens, it partakes of the color of both.”
—Henry David Thoreau (1817–1862)
“Virtue is the adherence in action to the nature of things, and the nature of things makes it prevalent. It consists in a perpetual substitution of being for seeming, and with sublime propriety God is described as saying, I A—.”
—Ralph Waldo Emerson (1803–1882)
“This was a great point gained; the archdeacon would certainly not come to morning service at Westminster Abbey, even though he were in London; and here the warden could rest quietly, and, when the time came, duly say his prayers.”
—Anthony Trollope (1815–1882)
“The temples, the tank, the jail, the palace, the birds, the carrion, the Guest House, that came into view as they issued from the gap and saw Mau beneath: they didn’t want it, they said in their hundred voices, “No, not yet,” and the sky said, “No, not there.””
—E.M. (Edward Morgan)