Organizers:

This meeting was the third Dagstuhl seminar which was concerned with the theory of computability and complexity over the real numbers. This theory, which is built on the Turing machine model, 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, numerica