AUTOMATIC MAPS IN EXOTIC NUMERATION SYSTEMS

Citation
Jp. Allouche et al., AUTOMATIC MAPS IN EXOTIC NUMERATION SYSTEMS, theory of computing systems, 30(3), 1997, pp. 285-331
Citations number
41
Categorie Soggetti
System Science",Mathematics,"Computer Science Theory & Methods",Mathematics
Journal title
Volume
30
Issue
3
Year of publication
1997
Pages
285 - 331
Database
ISI
SICI code
Abstract
We generalize the classical notion of a b-automatic sequence for a seq uence indexed by the natural numbers. We replace the integers by a sem iring and use a numeration system consisting of the powers of a base b and an appropriate set of digits. For example, we define (-3)-automat ic sequences (indexed by the ordinary integers or by the rational inte gers) and (-1 + i)-automatic sequences (indexed by the Gaussian intege rs). We show how these new notions are related to the old ones, and we study both the number-theoretic and automata-theoretic properties tha t permit the replacement of one numeration system by another.