Using approximation to relate computational classes over the reals

Abstract

We use our method of approximation to relate various classes of computable functions over the reals. In particular, we compare Computable Analysis to the two analog models, the General Purpose Analog Computer and Real Recursive Functions. There are a number of existing results in the literature showing that the different models correspond exactly. We show how these exact correspondences can be broken down into a two step process of approximation and completion. We show that the method of approximation has further application in relating classes of functions, exploiting the transitive nature of the approximation relation. This work builds on our earlier work with our method of approximation, giving more evidence of the breadth of its applicability. © Springer-Verlag Berlin Heidelberg 2007.