Émile Borel defined normality more than 100 years ago to formalize the most basic form of
randomness for real numbers. A number is normal to a given integer base if its expansion in …

This collaborative volume aims at presenting and developing recent trends at the interface
between the study of sequences, groups, and number theory, as the title may suggest. It is …

Finite-state dimension, introduced by Dai, Lathrop, Lutz and Mayordomo quantifies the
information rate in an infinite sequence as measured by finite-state automata. In this paper …

When presented with a string or sequence of zeros and ones, that is an element of {0, 1}≤
ω, it is often of interest to know how complex the object is. Was it created from some simple …

In this paper we characterize normal sequences and finite-state dimension in terms of the
automatic Kolmogorov complexity and finite-state a priori probability. We show that many …

In 2004, Dai, Lathrop, Lutz, and Mayordomo defined and investigated the finite-state
dimension (a finite-state version of algorithmic dimension) of a sequence S and, in 2018 …

We consider the previously defined notion of finite-state independence and we focus
specifically on normal words. We characterize finite-state independence of normal words in …

Given an integer b⩾ 2 b\geqslant2 and a set P \EuScriptP of prime numbers, the set TP
\EuScriptT_\EuScriptP of Toeplitz numbers comprises all elements of 0, b whose digits (an) …

We give metric theorems for the property of Borel normality for real numbers under the
assumption of digit dependencies in their expansion in a given integer base. We quantify …