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The cyclicity problem for the images of Q-rational series

Juha Honkala

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2011)

  • Volume: 45, Issue: 4, page 375-381
  • ISSN: 0988-3754

Abstract

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We show that it is decidable whether or not a given Q-rational series in several noncommutative variables has a cyclic image. By definition, a series r has a cyclic image if there is a rational number q such that all nonzero coefficients of r are integer powers of q.

How to cite

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Honkala, Juha. "The cyclicity problem for the images of Q-rational series." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 45.4 (2011): 375-381. <http://eudml.org/doc/273031>.

@article{Honkala2011,
abstract = {We show that it is decidable whether or not a given Q-rational series in several noncommutative variables has a cyclic image. By definition, a series r has a cyclic image if there is a rational number q such that all nonzero coefficients of r are integer powers of q.},
author = {Honkala, Juha},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {rational series; images of rational series; decidability; -rational series; set of coefficients of -rational series; non-commutative variables},
language = {eng},
number = {4},
pages = {375-381},
publisher = {EDP-Sciences},
title = {The cyclicity problem for the images of Q-rational series},
url = {http://eudml.org/doc/273031},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Honkala, Juha
TI - The cyclicity problem for the images of Q-rational series
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2011
PB - EDP-Sciences
VL - 45
IS - 4
SP - 375
EP - 381
AB - We show that it is decidable whether or not a given Q-rational series in several noncommutative variables has a cyclic image. By definition, a series r has a cyclic image if there is a rational number q such that all nonzero coefficients of r are integer powers of q.
LA - eng
KW - rational series; images of rational series; decidability; -rational series; set of coefficients of -rational series; non-commutative variables
UR - http://eudml.org/doc/273031
ER -

References

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  1. [1] J. Berstel and C. Reutenauer, Rational Series and Their Languages. Springer, Berlin (1988). Zbl0668.68005MR971022
  2. [2] J. Berstel and C. Reutenauer, Noncommutative Rational Series with Applications. Cambridge University Press, Cambridge (2011). Zbl1250.68007MR2760561
  3. [3] G. Jacob, La finitude des représentations linéaires des semi-groupes est décidable. J. Algebra52 (1978) 437–459. Zbl0374.20074MR473071
  4. [4] G. Polya, Arithmetische Eigenschaften der Reihenentwicklungen rationaler Funktionen. J. Reine Angew. Math.151 (1921) 1–31. Zbl47.0276.02JFM47.0276.02
  5. [5] A. Salomaa and M. Soittola, Automata-Theoretic Aspects of Formal Power Series. Springer, Berlin (1978). Zbl0377.68039MR483721
  6. [6] M.-P. Schützenberger, On the definition of a family of automata, Inf. Control4 (1961) 245–270. Zbl0104.00702MR135680

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