Two Characterizations of Finite-State Dimension
In this paper we provide two equivalent characterizations of the notion of finite-state dimension introduced by Dai, Lathrop, Lutz and Mayordomo . One of them uses Shannon’s entropy of non-aligned blocks and generalizes old results of Pillai  and Niven – Zuckerman . The second characterizes finite-state dimension in terms of superadditive functions that satisfy some calibration condition (in particular, superadditive upper bounds for Kolmogorov complexity). The use of superadditive bounds allows us to prove a general sufficient condition for normality that easily implies old results of Champernowne , Besicovitch , Copeland and Erdös , and also a recent result of Calude, Staiger and Stephan .