The General Purpose Analog Computer and Computable Analysis are Two Equivalent Paradigms of Analog Computation

  • Olivier Bournez
  • Manuel L. Campagnolo
  • Daniel S. Graça
  • Emmanuel Hainry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3959)


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.


Analog Computation Computable Analysis Turing Machine Recursive Function Computable Sequence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Olivier Bournez
    • 1
    • 6
  • Manuel L. Campagnolo
    • 2
    • 4
  • Daniel S. Graça
    • 3
    • 4
  • Emmanuel Hainry
    • 5
    • 6
  1. 1.INRIA Lorraine 
  2. 2.DM/ISAUniversidade Técnica de LisboaLisboaPortugal
  3. 3.DM/FCTUniversidade do Algarve, C. GambelasFaroPortugal
  4. 4.CLC, DM/ISTUniversidade Técnica de LisboaLisboaPortugal
  5. 5.Institut National Polytechnique de Lorraine 
  6. 6.Vandœuvre-Lès-NancyLORIA (UMR 7503 CNRS-INPL-INRIA-Nancy2-UHP), Campus scientifiqueFrance

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