On Sequences Defined by D0L Power Series

Issue		RAIRO-Theor. Inf. Appl. Volume 33, Number 2, March-April 1999


Page(s)		125 - 132
DOI		10.1051/ita:1999110

DOI: 10.1051/ita:1999110

Theoret. Informatics Appl. 33 (1999) 125-132

On Sequences Defined by D0L Power Series

Juha Honkala
Department of Mathematics, University of Turku, FIN-20014 Turku, Finland, and Turku Centre for Computer Science TUCS, FIN-20520 Turku, Finland; (juha.honkala@utu.fi)

Received May, 1998. Accepted December, 1998.

Abstract: We study D0L power series over commutative semirings. We show that a sequence $(c_n)_{n \geq 0}$ 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 $1 \leq i \leq k$ such that $c_{n+k}=c_{n+k-1}^{\beta_1}c_{n+k-2}^{\beta_2}\ldots c_n^{\beta_k}$ for all $n \geq 0$ . As a consequence we solve the equivalence problem of D0L power series over computable fields.

Keywords and phrases: D0L system, D0L power series.

AMS Subject Classification: 68Q45

Communicated by: J. Berstel.

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