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Erschienen in:
2006 | OriginalPaper | Buchkapitel
The General Purpose Analog Computer and Computable Analysis are Two Equivalent Paradigms of Analog Computation
verfasst von : Olivier Bournez, Manuel L. Campagnolo, Daniel S. Graça, Emmanuel Hainry
Erschienen in: Theory and Applications of Models of Computation
Verlag: Springer Berlin Heidelberg
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In this paper we revisit one of the first models of analog computation, Shannon’s General Purpose Analog Computer (GPAC). The GPAC has often been argued to be weaker than computable analysis. As main contribution, we show that if we change the notion of GPAC-computability in a natural way, we compute exactly all real computable functions (in the sense of computable analysis). Moreover, since GPACs are equivalent to systems of polynomial differential equations then we show that all real computable functions can be defined by such models.