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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; juha.honkala@utu.fi.
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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.

Information

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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References

J. Berstel and C. Reutenauer, Rational Series and Their Languages. Springer, Berlin (1988).
J. Honkala, On morphically generated formal power series. RAIRO, Theoret. Informatics Appl. 29 (1995) 105-127.
Honkala, J., On the decidability of some equivalence problems for L algebraic series. Intern. J. Algebra and Comput. 7 (1997) 339-351. CrossRef
J. Honkala, On D0L power series, Theoret. Comput. Sci., to appear.
W. Kuich and A. Salomaa, Semirings, Automata, Languages. Springer, Berlin (1986).
G. Rozenberg and A. Salomaa, The Mathematical Theory of L Systems. Academic Press, New York (1980).
G. Rozenberg and A. Salomaa, Eds., Handbook of Formal Languages 1-3 . Springer, Berlin (1997).
A. Salomaa and M. Soittola, Automata-Theoretic Aspects of Formal Power Series. Springer, Berlin (1978).