Klaus Ambos-Spies

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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)
Supported by the Human Capital and Mobility Program of the European Community under grant CHRX-CT93-0415 (COLORET). Mathematisches Institut, Universit at Heidelberg, D-69120 Heidelberg, Germany Universidad de Zaragoza, Dept. Inform atica, CPS, Mar a del Luna 3, E-50015 Zaragoza, Spain We survey recent results on resource-bounded measure and randomness in(More)
In this paper we investigate effective versions of Hausdorff 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 autoreducibility and immunity. By a new(More)
raet. A formal notion of diagonalization is developed which allows to enforce properties that are related to the class of polynomial timecomputable sets (the class of polynomial time computable functions respectively), like, e.g., p-immunity. It is shown that there are sets-called p-generiowhich have all properties enforceable by such diagonalizations. We(More)
We introduce balanced t(n)-genericity which is a reenement of the genericity concept of Ambos-Spies, Fleischhack and Huwig 2] and which in addition controls the frequency with which a condition is met. We show that this concept coincides with the resource-bounded version of Church's stochasticity 6]. By uniformly describing these concepts and weaker notions(More)