000162187 001__ 162187 000162187 005__ 20251017144559.0 000162187 0247_ $$2doi$$a10.1007/s00224-025-10227-w 000162187 0248_ $$2sideral$$a144776 000162187 037__ $$aART-2025-144776 000162187 041__ $$aeng 000162187 100__ $$aCalvert, Wesley 000162187 245__ $$aNormality, Relativization, and Randomness 000162187 260__ $$c2025 000162187 5203_ $$aNormal 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. 000162187 536__ $$9info:eu-repo/grantAgreement/ES/DGA/T64-20R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2019-104358RB-I00$$9info:eu-repo/grantAgreement/ES/MICINN/PID2022-138703OB-I00 000162187 540__ $$9info:eu-repo/semantics/closedAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000162187 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000162187 700__ $$aGruner, Emma 000162187 700__ $$0(orcid)0000-0002-9109-5337$$aMayordomo, Elvira$$uUniversidad de Zaragoza 000162187 700__ $$aTuretsky, Daniel 000162187 700__ $$aVillano, Java Darleen 000162187 7102_ $$15007$$2570$$aUniversidad de Zaragoza$$bDpto. Informát.Ingenie.Sistms.$$cÁrea Lenguajes y Sistemas Inf. 000162187 773__ $$g69, 3 (2025), [16 pp.]$$pTheor. Comput. Syst.$$tTHEORY OF COMPUTING SYSTEMS$$x1432-4350 000162187 8564_ $$s2934501$$uhttps://zaguan.unizar.es/record/162187/files/texto_completo.pdf$$yVersión publicada 000162187 8564_ $$s1326963$$uhttps://zaguan.unizar.es/record/162187/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000162187 909CO $$ooai:zaguan.unizar.es:162187$$particulos$$pdriver 000162187 951__ $$a2025-10-17-14:13:51 000162187 980__ $$aARTICLE