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Computation beyond the turing limit.

H T Siegelmann

    Science (New York, N.Y.)
    |April 28, 1995
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces the analog shift map, a chaotic dynamical system that exhibits super-Turing computational power, exceeding classical computation limits. This finding challenges the Church-Turing thesis and suggests new models for understanding physical phenomena.

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    Area of Science:

    • Theoretical Computer Science
    • Dynamical Systems Theory
    • Computational Physics

    Background:

    • The Church-Turing thesis posits that classical computation is the limit of what physical systems can compute.
    • Existing models of computation are based on classical physics.
    • The power of physical systems to compute remains an active area of research.

    Purpose of the Study:

    • To introduce a novel dynamical system, the analog shift map.
    • To demonstrate that this system possesses computational power beyond the Turing limit (super-Turing).
    • To explore the implications of this super-Turing system for understanding natural phenomena.

    Main Methods:

    • Description of the analog shift map, a simple yet chaotic dynamical system.
    • Analysis of the computational capabilities of the analog shift map.

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  • Comparison of its computational power to classical models and other computational paradigms.

    • Main Results:

    • The analog shift map exhibits computational power exceeding the Turing limit.
    • Its computation is analogous to that of neural networks and analog machines.
    • The system is conjectured to be a model for certain natural physical phenomena.

    Conclusions:

    • The analog shift map provides a concrete example of a super-Turing computational system.
    • This challenges the universality of the Church-Turing thesis in the context of physical systems.
    • The findings open new avenues for exploring computation in nature and advanced computing models.