Although numerous computer programs have been written to compute sets of points which claim to approximate Julia sets, no reliable high precision pictures of non-trivial Julia sets are currentlyâ€¦ (More)

A c.e. real x is Solovay reducible (S-reducible) to another c.e. real y if y is at least as difficult to be approximated as x. In this case, y is at least as random as x. Thus, the S-reducibilityâ€¦ (More)

A c.e. real x is Solovay reducible to another c.e. real y if x can be approximated at least as efficiently as y by means of increasing computable sequences of rational numbers. The Solovayâ€¦ (More)

The alternation hierarchy for Turing machines with a space bound between loglog and log is infinite. That applies to all common concepts, especially a) to two-way machines with weak space-bounds, b)â€¦ (More)

The computability of reals was introduced by Alan Turing [20] by means of decimal representations. But the equivalent notion can also be introduced accordingly if the binary expansion, Dedekind cutâ€¦ (More)

In this paper we will introduce well motivated definitions of computational complexity on type-2 objects. Similar to the model of Kawamura and Cook (and earlier models) our models will be both basedâ€¦ (More)