On sequences defined by D0L power series

: Honkala J

Publisher: GAUTHIER-VILLARS/EDITIONS ELSEVIER

: 1999

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

: RAIRO-INFORMATIQUE THEORIQUE ET APPLICATIONS-THEORETICAL INFORMATICS AND APPLICATIONS

: RAIRO-INF THEOR APPL

: 33

: 2

: 125

: 132

: 8

: 0988-3754

DOI: https://doi.org/10.1051/ita:1999110

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.