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

  • Authors:

  • Olivier Bournez;Manuel L. Campagnolo;Daniel S. Graça;Emmanuel Hainry

  • Affiliations:

  • INRIA Lorraine;DM/ISA, Universidade Técnica de Lisboa, Lisboa, Portugal;DM/FCT, Universidade do Algarve, C. Gambelas, Faro, Portugal;Institut National Polytechnique de Lorraine

  • Venue:
  • TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
  • Year:
  • 2006

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Abstract

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.