# On Sequences Defined by D0L Power Series

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 33, Issue: 2, page 125-132
- ISSN: 0988-3754

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topHonkala, Juha. "On Sequences Defined by D0L Power Series." RAIRO - Theoretical Informatics and Applications 33.2 (2010): 125-132. <http://eudml.org/doc/221981>.

@article{Honkala2010,

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 coefficient
sequence of a D0L power series if and only if there exist a positive integer
k 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 all
n ≥ 0. As a consequence we solve the equivalence problem of D0L power
series over computable fields.
},

author = {Honkala, Juha},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {D0L system; D0L power series.; D0L power series},

language = {eng},

month = {3},

number = {2},

pages = {125-132},

publisher = {EDP Sciences},

title = {On Sequences Defined by D0L Power Series},

url = {http://eudml.org/doc/221981},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Honkala, Juha

TI - On Sequences Defined by D0L Power Series

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 2

SP - 125

EP - 132

AB -
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 coefficient
sequence of a D0L power series if and only if there exist a positive integer
k 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 all
n ≥ 0. As a consequence we solve the equivalence problem of D0L power
series over computable fields.

LA - eng

KW - D0L system; D0L power series.; D0L power series

UR - http://eudml.org/doc/221981

ER -

## References

top- J. Berstel and C. Reutenauer, Rational Series and Their Languages. Springer, Berlin (1988). Zbl0668.68005
- J. Honkala, On morphically generated formal power series. RAIRO, Theoret. Informatics Appl.29 (1995) 105-127. Zbl0816.68077
- J. Honkala, On the decidability of some equivalence problems for L algebraic series. Intern. J. Algebra and Comput.7 (1997) 339-351. Zbl0879.68066
- J. Honkala, On D0L power series, Theoret. Comput. Sci., to appear. Zbl0945.68106
- 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). Zbl0508.68031
- G. Rozenberg and A. Salomaa, Eds., Handbook of Formal Languages 1-3. Springer, Berlin (1997). Zbl0866.68057
- A. Salomaa and M. Soittola, Automata-Theoretic Aspects of Formal Power Series. Springer, Berlin (1978). Zbl0377.68039

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