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The aim of CCA Network is to provide some useful information for researchers working in the field of computability and complexity in analysis. In particular, we offer: CCA Network is maintained by Vasco Brattka. Please, feel free to send any kind of suggestions and comments!

Computability and Complexity in Analysis

Computability theory and complexity theory are two central areas of research in mathematical logic and theoretical computer science. Computability theory is the study of the limitations and abilities of computers in principle. Computational complexity theory provides a framework for understanding the cost of solving computational problems, as measured by the requirement for resources such as time and space. The classical approach in these areas is to consider algorithms as operating on finite strings of symbols from a finite alphabet. Such strings may represent various discrete objects such as integers or algebraic expressions, but cannot represent a general real or complex number, unless it is rounded.

The classical theory of computation does not deal adequately with computations that operate on real-valued data. Most computational problems in the physical sciences and engineering are of this type, such as the complexity of network flow problems and of dynamical and hybrid systems. To study these types of problem, alternative models over real-valued data and other continuous structures have been developed in recent years. Unlike the well established classical theory of computation over discrete structures, the theory of computation over continuous data is still in its infancy.

Scientists working in the area of computation on real-valued data come from different fields, such as theoretical computer science, domain theory, logic, constructive mathematics, computer arithmetic, numerical mathematics, analysis, etc.

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