Computing with Polynomial Ordinary Differential Equations

@article{Bournez2016ComputingWP,
  title={Computing with Polynomial Ordinary Differential Equations},
  author={O. Bournez and D. Graça and A. Pouly},
  journal={ArXiv},
  year={2016},
  volume={abs/1601.05683}
}
  • O. Bournez, D. Graça, A. Pouly
  • Published 2016
  • Mathematics, Computer Science
  • ArXiv
  • In 1941, Claude Shannon introduced the General Purpose Analog Computer(GPAC) 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. Following Shannon's arguments, functions generated by GPACs must be differentially algebraic. As it is known that some computable functions like Euler's $\Gamma(x)=\int_{0}^{\infty}t^{x-1}e^{-t}dt$ or Riemann's Zeta function $\zeta(x)=\sum_{k=0}^\infty… CONTINUE READING
    5 Citations
    On the Functions Generated by the General Purpose Analog Computer
    • 12
    • PDF
    A Universal Ordinary Differential Equation
    • 9
    • PDF
    A Universal Ordinary Differential Equation
    • PDF
    Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length
    • 18
    • PDF

    References

    SHOWING 1-10 OF 34 REFERENCES
    On the Functions Generated by the General Purpose Analog Computer
    • 12
    • PDF
    Polynomial differential equations compute all real computable functions on computable compact intervals
    • 59
    • PDF
    Computational bounds on polynomial differential equations
    • 14
    • PDF
    Some recent developments on Shannon's General Purpose Analog Computer
    • 59
    • PDF
    Analog computers and recursive functions over the reals
    • 104
    • PDF
    New Computational Paradigms: Changing Conceptions of What is Computable
    • 100
    Recursion Theory on the Reals and Continuous-Time Computation
    • C. Moore
    • Mathematics, Computer Science
    • Theor. Comput. Sci.
    • 1996
    • 168
    • PDF
    Some Bounds on the Computational Power of Piecewise Constant Derivative Systems (Extended Abstract)
    • 12
    • PDF
    Coins, Quantum Measurements, and Turing's Barrier
    • 80
    • PDF