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Computation beyond the turing limit.

Science (New York, N.Y.)

|April 28, 1995

Summary

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.

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.