A1 Journal article – refereed

On sequences defined by D0L power series

List of Authors: Honkala J

Publisher: GAUTHIER-VILLARS/EDITIONS ELSEVIER

Publication year: 1999

Journal: RAIRO: Informatique Théorique et Applications / RAIRO: Theoretical Informatics and Applications

Journal name in source: RAIRO-INFORMATIQUE THEORIQUE ET APPLICATIONS-THEORETICAL INFORMATICS AND APPLICATIONS

Journal acronym: RAIRO-INF THEOR APPL

Volume number: 33

Issue number: 2

Number of pages: 8

ISSN: 0988-3754

Abstract

We study D0L power series over commutative semirings. We show that a sequence (c(n))(n greater than or equal to 0) of nonzero elements of a field A is the coefficient sequence of a D0L power series if and only if there exist a positive integer k and integers beta(i) for 1 less than or equal to i less than or equal to k such that c(n+k) = c(n+k-1)(beta 1) c(n+k-2)(beta 2) ... c(n)(beta k) for all n greater than or equal to 0. As a consequence we solve the equivalence problem of D0L power series over computable fields.