![]() Let F be the Thue-Morse set and let A be the automaton ![]() With the states of the minimal automaton indicated on its prefixes. The F-maximal bifix code X has 8 elements. Generating the submonoid stabilizing 1 and let X = Z ∩ F. I ≥ j, ψ i, j ∘ Ψ i = Ψ j, there is a morphism We also apply similar ideas to create computably-invariant restrictions of the generic-case computability defined by Jockusch and Schupp, and prove a generalization of Rice's Theorem as a lower bound on their strength.For any A-generated topological semigroup Ψ : A → T In particular, we use it to define a new immunity property, recognize a new form of stochasticity, and find an unexpected connection to functions avoiding weak computable approximation. ![]() We investigate a computably-invariant restriction of asymptotic density, and observe that it has strong connections to both randomness and classical computability theory. Org: Peter Cholak (Notre Dame) and Barbara Csima (Waterloo)Īsymptotic density, immunity, and randomness ![]()
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