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arXiv · 2302.06444

Symmetry for transfinite computability

Lorenzo Galeotti·Ethan S. Lewis·Benedikt Löwe
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Abstract

Finite Turing computation has a fundamental symmetry between inputs, outputs, programs, time, and storage space. Standard models of transfinite computational break this symmetry; we consider ways to recover it and study the resulting model of computation. This model exhibits the same symmetry as finite Turing computation in universes constructible from a set of ordinals, but that statement is independent of von Neumann-G\"odel-Bernays class theory.

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Lorenzo Galeotti, Ethan S. Lewis, Benedikt Löwe. 2023-02-13. Symmetry for transfinite computability. https://arxiv.org/abs/2302.06444

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