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

摘要

In this paper we revisit one of the rst models of analogcomputation, 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 GPACcomputabilityin a natural way, we compute exactly all real computablefunctions (in the sense of computable analysis). Moreover, since GPACsare equivalent to systems of polynomial di erential equations then weshow that all real computable functions can be de ned by such models.