Strong jump traceability and Demuth randomness
Noam Greenberg, Daniel Turetsky
TL;DR
This paper characterizes the relationship between Demuth randomness and strong jump traceability, establishing a precise equivalence for c.e. sets and clarifying the class of Demuth randomness bases.
Contribution
It proves that a c.e. set is computable from a Demuth random set if and only if it is strongly jump-traceable, and shows the class of Demuth randomness bases is a proper subset of strongly jump-traceable sets.
Findings
A c.e. set is computable from a Demuth random set iff it is strongly jump-traceable.
The class of Demuth randomness bases is a proper subclass of strongly jump-traceable sets.
Abstract
We solve the covering problem for Demuth randomness, showing that a computably enumerable set is computable from a Demuth random set if and only if it is strongly jump-traceable. We show that on the other hand, the class of sets which form a base for Demuth randomness is a proper subclass of the class of strongly jump-traceable sets.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Logic, Reasoning, and Knowledge · Cryptography and Data Security