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Updated: May 21, 2026

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One Dimensional Turing-Like Handshake Test for Motor Intelligence
Published on: December 15, 2010
The physical Church-Turing thesis and non-deterministic computation over the real numbers.
1INRIA, Paris, France. gilles.dowek@inria.fr
Summary
Effectively enumerable relations, not semi-decidable ones, are suitable for algorithmically describing non-deterministic physical theories using real numbers.
Area of Science:
- Theoretical Computer Science
- Mathematical Physics
Background:
- Distinctions exist between semi-decidable and effectively enumerable relations on real numbers.
- Current algorithmic frameworks may not fully capture the complexity of non-deterministic physical theories.
Purpose of the Study:
- To clarify the difference between semi-decidable and effectively enumerable relations.
- To establish the suitability of effectively enumerable relations for algorithmic representations of non-deterministic physical theories.
Main Methods:
- Comparative analysis of formal definitions of semi-decidability and effective enumerability.
- Exploration of the implications of these definitions for representing real numbers in algorithmic models.
Main Results:
- Semi-decidable and effectively enumerable relations exhibit distinct properties when applied to the real number system.
- Effectively enumerable relations provide a more appropriate framework for algorithmic descriptions in non-deterministic physical theories.
Conclusions:
- The choice of relation is critical for accurately modeling non-deterministic physical theories algorithmically.
- Effectively enumerable relations are better suited for expressing non-deterministic physical theories involving real numbers.
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