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

RAIRO - Theoretical Informatics and Applications (2012)

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

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