Disjunctive Sequences: An Overview (1997)
BibTeX
@MISC{Calude97disjunctivesequences:,
author = {Cristian S. Calude and Lutz Priese and Ludwig Staiger},
title = {Disjunctive Sequences: An Overview},
year = {1997}
}
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Abstract
Following Jürgensen and Thierrin [21] we say that an infinite sequence is disjunctive if it contains any (finite) word, or, equivalently, if any word appears in the sequence infinitely many times. "Disjunctivity" is a natural qualitative property; it is weaker, than the property of "normality" (introduced by Borel [1]; see, for instance, Kuipers, Niederreiter [24]). The aim of this paper is to survey some basic results on disjunctive sequences and to explore their role in various areas of mathematics (e.g. in automata-theoretic studies of #-languages or number theory). To achieve our goal we will use various instruments borrowed from topology, measure-theory, probability theory, number theory, automata and formal languages.
