Lowness, randomness, and computable analysis
Andr\'e Nies
TL;DR
This paper surveys how analytic concepts in computable analysis relate to randomness and lowness notions, highlighting their interplay and significance in understanding the randomness of real numbers.
Contribution
It provides a comprehensive survey of the connections between analytic concepts, randomness, and lowness in computable analysis, on the occasion of Rod Downey's 60th birthday.
Findings
Analytic concepts help characterize randomness of reals.
The interplay between randomness and lowness notions is influenced by analytic ideas.
The survey summarizes key developments in the field.
Abstract
Analytic concepts contribute to our understanding of randomness of reals via algorithmic tests. They also influence the interplay between randomness and lowness notions. We provide a survey, written on the occasion of Rod Downey's 60th birthday.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Benford’s Law and Fraud Detection · Algorithms and Data Compression