Abstract Computability and Its Relation to the General Purpose Analog Computer (Some Connections Between Logic, Differential Equations and Analog Computers)

DOI10.2307/1996870zbMath0296.02022OpenAlexW4239360595MaRDI QIDQ4049052

Marian Boykan Pour-El

Publication date: 1974

Full work available at URL: https://doi.org/10.2307/1996870

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Applications of computability and recursion theory (03D80) Computability and recursion theory (03D99) Computability and recursion theory on ordinals, admissible sets, etc. (03D60)

Related Items (34)

An analog characterization of the Grzegorczyk hierarchy ⋮ The complexity of analog computation ⋮ Polynomial differential equations compute all real computable functions on computable compact intervals ⋮ Computing with polynomial ordinary differential equations ⋮ Recursion theory on the reals and continuous-time computation ⋮ Real-time computability of real numbers by chemical reaction networks ⋮ Can Newtonian systems, bounded in space, time, mass and energy compute all functions? ⋮ Computability of analog networks ⋮ Some mathematical limitations of the general-purpose analog computer ⋮ On the functions generated by the general purpose analog computer ⋮ Computations with oracles that measure vanishing quantities ⋮ Physical Computability Theses ⋮ Recursive analysis of singular ordinary differential equations ⋮ Solutions of algebraic differential equations ⋮ Construction of a universal ordinary differential equation \(C^{\infty}\) of order 3 ⋮ Analog computers and recursive functions over the reals. ⋮ Natural computation and non-Turing models of computation ⋮ A Differentially Algebraic Elimination Theorem with Application to Analog Computability in the Calculus of Variations ⋮ Iteration, inequalities, and differentiability in analog computers ⋮ Characterizing Computable Analysis with Differential Equations ⋮ Computability with polynomial differential equations ⋮ A survey of recursive analysis and Moore's notion of real computation ⋮ Real recursive functions and their hierarchy ⋮ A Universal Ordinary Differential Equation ⋮ Embedding infinitely parallel computation in Newtonian kinematics ⋮ Analog computation beyond the Turing limit ⋮ A new conceptual framework for analog computation ⋮ Computational bounds on polynomial differential equations ⋮ A universal differential equation ⋮ Analog computation with dynamical systems ⋮ Elementarily computable functions over the real numbers and \(\mathbb R\)-sub-recursive functions ⋮ A theory of complexity for continuous time systems ⋮ A Survey on Analog Models of Computation ⋮ Some Research Problems about Algebraic Differential Equations

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• An Unsolvable Problem of Elementary Number Theory
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• Nicht konstruktiv beweisbare Sätze der Analysis
• Recursive Real Numbers
• Mathematical Theory of the Differential Analyzer

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