November 14 – 19 , 1999, Dagstuhl Seminar 99461

Computability and Complexity in Analysis


Ker-I Ko (Stony Brook), A. Nerode (Ithaka), K. Weihrauch (Hagen)

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Dagstuhl-Seminar-Report 259


Already for a long time physicists, engineers, mathematicians and other scientists are spending large amounts of computing resources on computations over the real numbers. So far computer scientists deal mainly with computations over discrete, countable structures. But increasingly they too are confronted with problems involving real numbers and continuous structures (for example the complexity theoretic analysis of numerical problems, modeling of continuous or partially continuous signals and processes, hybrid systems, computation problems connected with dynamical systems, computational geometry). In order to deal with these problems one has to find effective analogues of results in classical analysis, to classify problems in the framework of computability theory, and to analyze their complexity. It also still requires a careful discussion of suitable models and work on the foundations of computability over the real numbers.

In this seminar the emphasis will be put on computable analysis which was initiated by Turing and Grzegorczyk and which is based on the Turing machine model.

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