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On Sequences Defined by D0L Power Series

Published online by Cambridge University Press:  15 August 2002

Juha Honkala
Juha Honkala*
Affiliation:
Department of Mathematics, University of Turku, FIN-20014 Turku, Finland, and Turku Centre for Computer Science TUCS, FIN-20520 Turku, Finland; [email protected].
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Abstract

We study D0L power series over commutative semirings. We show that a sequence(cn )n≥0 of nonzero elements of a field A is the coefficientsequence of a D0L power series if and only if there exist a positive integerk and integers βi for 1 ≤ i ≤ k such that $c_{n+k}=c_{n+k-1}^{\beta_1}c_{n+k-2}^{\beta_2}\ldots c_n^{\beta_k}$ for alln ≥ 0. As a consequence we solve the equivalence problem of D0L powerseries over computable fields.

Keywords

D0L systemD0L power series.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 2 , March 1999 , pp. 125 - 132
Copyright
© EDP Sciences, 1999

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