2011/10/23 by Laurent Bienvenu, Alexander Shen, Bienvenu, Laurent +1
Computer Science · Mathematics · #03D32 #68Q30 #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #F.1 #FOS: Mathematics #Logic (math.LO) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1110.5028
openalex publication_date 2011/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this expository paper is to present a nice series of results, obtained in the papers of Chaitin (1976), Solovay (1975), Calude et al. (1998), Kucera and Slaman (2001). This joint effort led to a full characterization of lower semicomputable random reals, both as those that can be expressed as a "Chaitin Omega" and those that are maximal for the Solovay reducibility. The original proofs were somewhat involved; in this paper, we present these results in an elementary way, in particular requiring only basic knowledge of algorithmic randomness. We add also several simple observations relating lower semicomputable random reals and busy beaver functions.