Abstract computability and its relation to the general purpose analog computer (some connections between logic, differential equations and analog computers)

@article{PourEl1974AbstractCA,
  title={Abstract computability and its relation to the general purpose analog computer (some connections between logic, differential equations and analog computers)},
  author={M. B. Pour-El},
  journal={Transactions of the American Mathematical Society},
  year={1974},
  volume={199},
  pages={1-28}
}
  • M. B. Pour-El
  • Published 1974
  • Mathematics
  • Transactions of the American Mathematical Society
  • COMPUTABILITY AND ITS RELATION TO THE GENERAL PURPOSE ANALOG COMPUTER (SOME CONNECTIONS BETWEEN LOGIC, DIFFERENTIAL EQUATIONS AND ANALOG COMPUTERS) BY MARIAN BOYKAN POUR-EL(l) ABSTRACT. Our aim is to study computability from the viewpoint of the analog computer. We present a mathematical definition of an analog generable function of a real variable. This definition is formulated in terms of a simultaneous set of nonlinear differential equations possessing a "domain of generation." (The latter… CONTINUE READING
    163 Citations
    On the Functions Generated by the General Purpose Analog Computer
    • 12
    • Highly Influenced
    • PDF
    Real recursive functions and their hierarchy
    • 52
    • PDF
    Digital Simulation of Analog Computation and Church's Thesis
    • L. Rubel
    • Computer Science, Mathematics
    • J. Symb. Log.
    • 1989
    • 43
    Computing with Polynomial Ordinary Differential Equations
    • 5
    • PDF
    Computational bounds on polynomial differential equations
    • 14
    • PDF
    Some recent developments on Shannon's General Purpose Analog Computer
    • 59
    • PDF
    An Analog Characterization of the Grzegorczyk Hierarchy
    • 65

    References

    SHOWING 1-10 OF 19 REFERENCES
    Recursive real numbers
    • 126
    • PDF
    IV. On an instrument for calculating (∫φ(x) ψ (x)dx), the integral of the product of two given functions
    • W. Thomson
    • Computer Science
    • Proceedings of the Royal Society of London
    • 1876
    • 25
    • PDF
    Analog Computer Techniques
    • 75
    • Highly Influential
    The Theory of Algorithms
    • 220
    An Unsolvable Problem of Elementary Number Theory
    • 1,458
    • PDF
    Electronic analog and hybrid computers
    • 154
    Nicht Konstruktiv Beweisbare Satze Der Analysis
    • E. Specker
    • Mathematics, Computer Science
    • J. Symb. Log.
    • 1949
    • 272
    • PDF
    High-speed analog computers
    • 8
    Apóstol, Mathematical analysis: A modem approach to advanced calculus, Addison-Wesley, Reading, Mass., 1957
    • MR
    • 1957