RELATIVE RANDOMNESS VIA RK - REDUCIBILITY by Alexander Raichev A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy ( Mathematics ) at the UNIVERSITY OF WISCONSIN - MADISON 2006
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چکیده
This is a dissertation in the field of Mathematics: Logic: Computability Theory: Algorithmic Randomness (Mathematics Subject Classification 03D80, 68Q30). Its focus is relative randomness as measured by rK-reducibility, a refinement of Turing reducibility defined as follows. An infinite binary sequence A is rK-reducible to an infinite binary sequence B, written A ≤rK B, if ∃d ∀n . K(A n|B n) < d, where K(σ|τ) is the conditional prefix-free descriptional complexity of σ given τ . Herein i study the relationship between relative randomness and (standard) absolute randomness and that between relative randomness and computable analysis.
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