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- Klaus Ambos-Spies, Anton N Ku
- 2000

We discuss some aspects of algorithmic randomness and state some open problems in this area. The rst part is devoted to the question \What is a computably random sequence?" Here we survey some of the approaches to algorithmic randomness and address some questions on these concepts. In the second part we look at the Turing degrees of Martin-LL of random… (More)

In this paper we investigate effective versions of Haus-dorff dimension which have been recently introduced by Lutz. We focus on dimension in the class E of sets computable in linear exponential time. We determine the dimension of various classes related to fundamental structural properties including different types of autoreducibil-ity and immunity. By a… (More)

We survey recent results on resource-bounded measure and random-ness in structural complexity theory. In particular, we discuss applications of these concepts to the exponential time complexity classes E and E2. Moreover, we treat time-bounded genericity and stochasticity concepts which are weaker than time-bounded randomness but which suuce for many of the… (More)

In Reverse Mathematics, the axiom system DNR, asserting the existence of diagonally non-recursive functions, is strictly weaker than WWKL0 (weak weak König's Lemma). §1. Introduction. Reverse mathematics is a branch of proof theory which involves proving the equivalence of mathematical theorems with certain collections of axioms over a weaker base theory.… (More)