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Some representations for series on idempotent semirings - or how to go beyond recognizability keeping representability
Kybernetika, Tome 39 (2003) no. 2, pp. 177-192 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this article, we compare different types of representations for series with coefficients in complete idempotent semirings. Each of these representations was introduced to solve a particular problem. We show how they are or are not included one in the other and we present a common generalization of them.
In this article, we compare different types of representations for series with coefficients in complete idempotent semirings. Each of these representations was introduced to solve a particular problem. We show how they are or are not included one in the other and we present a common generalization of them.
Classification : 13F25, 93B25, 93C65
Keywords: idempotent semirings; recognizable series 
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     title = {Some representations for series on idempotent semirings - or how to go beyond recognizability keeping representability},
     journal = {Kybernetika},
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}
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Klimann, Ines. Some representations for series on idempotent semirings - or how to go beyond recognizability keeping representability. Kybernetika, Tome 39 (2003) no. 2, pp. 177-192. http://geodesic.mathdoc.fr/item/KYB_2003_39_2_a7/

[1] Berstel J.: Transductions and Context–Free Languages. Teubner, Stuttgart 1979 | MR | Zbl

[2] Berstel J., Reutenauer C.: Les séries rationnelles et leurs langages. Masson, Paris 1984. English translation: Rational Series and Their Languages, Springer–Verlag, Berlin 1988 | MR | Zbl

[3] Blyth T. S., Janowitz M. F.: Residuation Theory. Pergamon Press, Oxford 1972 | MR | Zbl

[4] Eilenberg S.: Automata, Languages and Machines, vol. A. Academic Press, New York 1974 | MR | Zbl

[5] Gunawardena J.: An introduction to idempotency, in idempotency. Chapter 1 (J. Gunawardena, ed.), Cambridge University Press, Cambridge 1998 | MR

[6] Klimann I.: New types of automata to solve fixed point problems. Theoret. Comput. Sci. 259 (2001), 1–2, 183–197 | DOI | MR | Zbl

[7] Klimann I.: A solution to the problem of $(A,B)$-invariance for series. Theoret. Comput. Sci. 293 (2003), 1, 115–139 | DOI | MR | Zbl

[8] Kobayashi N.: The closure under division and a characterization of the recognizable ${\mathcal Z}$-subsets. RAIRO Inform. Théor. Appl. 30 (1996), 3, 209–230 | MR

[9] Pin J.-E., Sakarovitch J.: Une application de la représentation matricielle des transductions. Theoret. Comp. Sci. 35 (1985), 271–293 | DOI | MR | Zbl

[10] Salomaa A., Soittola M.: Automata–Theoretical Aspects of Formal Power Series. Springer–Verlag, Berlin 1978 | MR