This Dagstuhl seminar is concerned with the theory of computability and complexity over the real numbers which is built on the Turing machine model. This theory was initiated by Turing, Grzegorczyk, Lacombe, Banach and Mazur, and has seen a rapid growth in recent years. Recent monographs are by Pour-El/Richards, Ko, and Weihrauch.

Computability theory and complexity theory are two central areas of research in theoretical computer science. Until recently, most work in these areas concentrated on problems over discrete structures. In the last years, though, there has been an enormous growth of computability theory and complexity theory over the real numbers and other continuous structures. One of the reasons for this phenomenon is that more and more practical computation problems over the real numbers are being dealt with by computer scientists, for example, in computational geometry, in the modelling of dynamical and hybrid systems, but also in classical problems from numerical mathematics. The scientists working on these questions come from different fields, such as theoretical computer science, domain theory, logic, constructive mathematics, computer arithmetic, numerical mathematics, analysis etc.

The Dagstuhl seminar provides a unique opportunity for people from such diverse areas to meet and exchange ideas and knowledge. One of the topics of interest is foundational work concerning the various models and approaches for defining or describing computability and complexity over the real numbers. We also hope to gain new insights into the computability--theoretic side of various computational questions from physics as well as from other fields involving computations over the real numbers. This, of course, also requires the extension of existing computability notions to more general classes of objects. Other topics of interest are complexity--theoretic investigations, both foundational and with respect to concrete problems. Last but not least, new implementations of exact real arithmetic and further developments of already existing software packages will be of interest.