| Title:
|
Some representations for series on idempotent semirings - or how to go beyond recognizability keeping representability (English) |
| Author:
|
Klimann, Ines |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
[177]-192 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
idempotent semirings |
| Keyword:
|
recognizable series |
| MSC:
|
13F25 |
| MSC:
|
93B25 |
| MSC:
|
93C65 |
| idZBL:
|
Zbl 1249.93043 |
| idMR:
|
MR1996556 |
| . |
| Date available:
|
2009-09-24T19:52:37Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135520 |
| . |
| Reference:
|
[1] Berstel J.: Transductions and Context–Free Languages.Teubner, Stuttgart 1979 Zbl 0424.68040, MR 0549481 |
| Reference:
|
[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 Zbl 0573.68037, MR 0971022 |
| Reference:
|
[3] Blyth T. S., Janowitz M. F.: Residuation Theory.Pergamon Press, Oxford 1972 Zbl 0301.06001, MR 0396359 |
| Reference:
|
[4] Eilenberg S.: Automata, Languages and Machines, vol.A. Academic Press, New York 1974 Zbl 0359.94067, MR 0530382 |
| Reference:
|
[5] Gunawardena J.: An introduction to idempotency, in idempotency.Chapter 1 (J. Gunawardena, ed.), Cambridge University Press, Cambridge 1998 MR 1608370 |
| Reference:
|
[6] Klimann I.: New types of automata to solve fixed point problems.Theoret. Comput. Sci. 259 (2001), 1–2, 183–197 Zbl 0973.68122, MR 1832790, 10.1016/S0304-3975(99)00335-7 |
| Reference:
|
[7] Klimann I.: A solution to the problem of $(A,B)$-invariance for series.Theoret. Comput. Sci. 293 (2003), 1, 115–139 Zbl 1025.68050, MR 1957615, 10.1016/S0304-3975(02)00234-7 |
| Reference:
|
[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 1415829 |
| Reference:
|
[9] Pin J.-E., Sakarovitch J.: Une application de la représentation matricielle des transductions.Theoret. Comp. Sci. 35 (1985), 271–293 Zbl 0563.68064, MR 0785156, 10.1016/0304-3975(85)90019-2 |
| Reference:
|
[10] Salomaa A., Soittola M.: Automata–Theoretical Aspects of Formal Power Series.Springer–Verlag, Berlin 1978 MR 0483721 |
| . |
