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On sequences defined by D0L power series
Tekijät: Honkala J
Kustantaja: GAUTHIER-VILLARS/EDITIONS ELSEVIER
Julkaisuvuosi: 1999
Journal: RAIRO: Informatique Théorique et Applications / RAIRO: Theoretical Informatics and Applications
Tietokannassa oleva lehden nimi: RAIRO-INFORMATIQUE THEORIQUE ET APPLICATIONS-THEORETICAL INFORMATICS AND APPLICATIONS
Lehden akronyymi: RAIRO-INF THEOR APPL
Vuosikerta: 33
Numero: 2
Aloitussivu: 125
Lopetussivu: 132
Sivujen määrä: 8
ISSN: 0988-3754
DOI: https://doi.org/10.1051/ita:1999110
Tiivistelmä
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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