A DNC function that computes no effectively bi-immune set
Achilles A. Beros
TL;DR
This paper constructs a specific diagonally non-computable (DNC) function that does not compute any effectively bi-immune set, answering a question about the computational power of DNC functions.
Contribution
It provides a counterexample DNC function that fails to compute any effectively bi-immune set, challenging previous assumptions.
Findings
Constructed a DNC function with no effectively bi-immune set
Answered a longstanding open question in computability theory
Clarified the limitations of DNC functions in computing bi-immune sets
Abstract
In Diagonally Non-Computable Functions and Bi-Immunity, Carl Jockusch and Andrew Lewis proved that every DNC function computes a bi-immune set. They asked whether every DNC function computes an effectively bi-immune set. We construct a DNC function that computes no effectively bi-immune set, thereby answering their question in the negative.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Benford’s Law and Fraud Detection · semigroups and automata theory