162187 20260316125346.0 doi 10.1007/s00224-025-10227-w sideral 144776 ART-2025-144776 eng Calvert, Wesley Normality, Relativization, and Randomness 2025 Access copy available to the general public Unrestricted Normal numbers were introduced by Borel and later proven to be a weak notion of algorithmic randomness. We introduce here a natural relativization of normality based on generalized number representation systems. We explore the concepts of supernormal numbers that correspond to semicomputable relativizations, and that of highly normal numbers in terms of computable ones. We prove several properties of these new randomness concepts. Both supernormality and high normality generalize Borel absolute normality. Supernormality is strictly between 2-randomness and effective dimension 1, while high normality corresponds exactly to sequences of computable dimension 1 providing a more natural characterization of this class. info:eu-repo/grantAgreement/ES/DGA/T64-20R info:eu-repo/grantAgreement/ES/MICINN/PID2019-104358RB-I00 info:eu-repo/grantAgreement/ES/MICINN/PID2022-138703OB-I00 info:eu-repo/semantics/embargoedAccess All rights reserved http://www.europeana.eu/rights/rr-f/ info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Gruner, Emma Mayordomo, Elvira Universidad de Zaragoza (orcid)0000-0002-9109-5337 Turetsky, Daniel Villano, Java Darleen 5007 570 Universidad de Zaragoza Dpto. Informát.Ingenie.Sistms. Área Lenguajes y Sistemas Inf. 69, 3 (2025), [16 pp.] Theor. Comput. Syst. THEORY OF COMPUTING SYSTEMS 1432-4350 328934 http://zaguan.unizar.es/record/162187/files/texto_completo.pdf Postprint info:eu-repo/date/embargoEnd/2026-06-21 1151429 http://zaguan.unizar.es/record/162187/files/texto_completo.jpg?subformat=icon icon Postprint info:eu-repo/date/embargoEnd/2026-06-21 oai:zaguan.unizar.es:162187 articulos driver 2026-03-16-08:29:34 ARTICLE