# The cyclicity problem for the images of Q-rational series

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

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

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

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