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Complexity in the Real world

By Chris Heunen

Abstract

Whereas Turing Machines lay a solid foundation for computation of functions on countable sets, a lot of real-world calculations require real numbers. The question arises naturally whether there is a satisfying extension to functions on uncountable sets. This thesis states and discusses such a generalization, based on previous research. It also discusses higher order functions, e.g. differentiation. In contrast to preceding works, however, the focus is on complexity – after computability, of course. By giving a different perspective on Weihrauch’s excellent definition of computability in the uncountable case, we show that this theory indeed admits a useful notion of complexity. Various examples are given to demonstrate the theory, including an application to distributions, also called generalized functions, as a form of ‘stress-test’

Year: 2005
OAI identifier: oai:CiteSeerX.psu:10.1.1.189.5239
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