The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation

Bournez, Olivier; Campagnolo, Manuel; Graça, Daniel; Hainry, Emmanuel

http://hdl.handle.net/10400.1/1009

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In this paper we revisit one of the rst 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 GPACcomputability 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 di erential equations then we show that all real computable functions can be de ned by such models.