Skip to main content
Article thumbnail
Location of Repository

Regular Maps in Generalized Number Systems

By J.-P. Allouche, K. Scheicher and R. F. Tichy


This paper extends some results of Allouche and Shallit for q-regular sequences to numeration systems in algebraic number fields and to linear numeration systems. We also construct automata that perform addition and multiplication by a fixed number. 1 Introduction A sequence is called q-automatic if its n-th term can be generated by a finite state machine from the q-ary digits of n. The concept of automatic sequences was introduced in 1969 and 1972 by Cobham [8, 9]. In 1979 Christol [6] (see also Christol, Kamae, Mend`es France and Rauzy [7]) discovered a nice arithmetic property of automatic sequences: a sequence with values in a finite field of characteristic p is p-automatic if and only if the corresponding power series is algebraic over the field of rational functions over this finite field. A brief survey on this subject is given in [2], see also [10]. Some generalizations of this concept were studied in [27, 23, 24, 3], see also the survey [1]. An automatic sequence has to t..

Year: 2000
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.