On Sequences Defined by D0L Power Series

Juha Honkala

RAIRO - Theoretical Informatics and Applications (2010)

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

Abstract

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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 β 1 c n + k - 2 β 2 ... c n β k for all n ≥ 0. As a consequence we solve the equivalence problem of D0L power series over computable fields.

How to cite

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Honkala, 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

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  1. J. Berstel and C. Reutenauer, Rational Series and Their Languages. Springer, Berlin (1988).  Zbl0668.68005
  2. J. Honkala, On morphically generated formal power series. RAIRO, Theoret. Informatics Appl.29 (1995) 105-127.  Zbl0816.68077
  3. J. Honkala, On the decidability of some equivalence problems for L algebraic series. Intern. J. Algebra and Comput.7 (1997) 339-351.  Zbl0879.68066
  4. J. Honkala, On D0L power series, Theoret. Comput. Sci., to appear.  Zbl0945.68106
  5. W. Kuich and A. Salomaa, Semirings, Automata, Languages. Springer, Berlin (1986).  
  6. G. Rozenberg and A. Salomaa, The Mathematical Theory of L Systems. Academic Press, New York (1980).  Zbl0508.68031
  7. G. Rozenberg and A. Salomaa, Eds., Handbook of Formal Languages 1-3. Springer, Berlin (1997).  Zbl0866.68057
  8. A. Salomaa and M. Soittola, Automata-Theoretic Aspects of Formal Power Series. Springer, Berlin (1978).  Zbl0377.68039

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