The cyclicity problem for the images of Q-rational series

Juha Honkala

RAIRO - Theoretical Informatics and Applications (2012)

  • 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 45.4 (2012): 375-381. <http://eudml.org/doc/221994>.

@article{Honkala2012,
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},
keywords = {Rational series; images of rational series; decidability; -rational series; set of coefficients of -rational series; non-commutative variables},
language = {eng},
month = {1},
number = {4},
pages = {375-381},
publisher = {EDP Sciences},
title = {The cyclicity problem for the images of Q-rational series},
url = {http://eudml.org/doc/221994},
volume = {45},
year = {2012},
}

TY - JOUR
AU - Honkala, Juha
TI - The cyclicity problem for the images of Q-rational series
JO - RAIRO - Theoretical Informatics and Applications
DA - 2012/1//
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/221994
ER -

References

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

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