On the Functions Generated by the General Purpose Analog Computer

@article{Bournez2017OnTF,
  title={On the Functions Generated by the General Purpose Analog Computer},
  author={O. Bournez and D. Graça and A. Pouly},
  journal={Inf. Comput.},
  year={2017},
  volume={257},
  pages={34-57}
}
  • O. Bournez, D. Graça, A. Pouly
  • Published 2017
  • Mathematics, Computer Science
  • Inf. Comput.
  • We consider the General Purpose Analog Computer (GPAC), introduced by Claude Shannon in 1941 as a mathematical model of Differential Analysers, that is to say as a model of continuous-time analog (mechanical, and later one electronic) machines of that time. We extend the model properly to a model of computation not restricted to univariate functions (i.e. functions $f: \mathbb{R} \to \mathbb{R}$) but also to the multivariate case of (i.e. functions $f: \mathbb{R}^n \to \mathbb{R}^m$), and… CONTINUE READING
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    References

    SHOWING 1-10 OF 32 REFERENCES
    Computing with Polynomial Ordinary Differential Equations
    • 4
    • PDF
    Some recent developments on Shannon's General Purpose Analog Computer
    • 59
    • PDF
    Analog computers and recursive functions over the reals
    • 104
    • Highly Influential
    • PDF
    Polynomial differential equations compute all real computable functions on computable compact intervals
    • 59
    • PDF
    Analog networks on function data streams
    • 2
    • Highly Influential
    • PDF
    Complexity Theory of Real Functions
    • K. Ko
    • Mathematics, Computer Science
    • Progress in Theoretical Computer Science
    • 1991
    • 506
    The differential analyzer. A new machine for solving differential equations
    • 163
    • PDF
    A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS
    • 2,753
    • PDF