A1 Refereed original research article in a scientific journal
On sequences defined by D0L power series
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: 33
Issue: 2
First page : 125
Last page: 132
Number of pages: 8
ISSN: 0988-3754
DOI: https://doi.org/10.1051/ita:1999110(external)
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.
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.
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