Weihrauch-completeness for layerwise computability
Arno Pauly, Willem Fouch\'e, George Davie
TL;DR
This paper introduces Weihrauch-completeness for layerwise computability, providing examples related to complex oscillations, the law of the iterated logarithm, and Birkhoff's theorem, and analyzes hitting time operators.
Contribution
It defines Weihrauch-completeness for layerwise computability and explores its applications and limitations through natural examples and operators.
Findings
Examples related to complex oscillations and classical theorems are Weihrauch-complete.
Hitting time operators share the same Weihrauch degree but are not layerwise computable.
The paper clarifies the relationship between Weihrauch degrees and layerwise computability.
Abstract
We introduce the notion of being Weihrauch-complete for layerwise computability and provide several natural examples related to complex oscillations, the law of the iterated logarithm and Birkhoff's theorem. We also consider hitting time operators, which share the Weihrauch degree of the former examples but fail to be layerwise computable.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Advanced Algebra and Logic