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On abstract families of languages, power series, and elements

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Foundations of Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1337))

Abstract

We generalize the characterization of abstract families of languages by abstract families of acceptors to continuous semirings: Abstract families of elements are now characterized by automata representing a certain type.

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References

  1. Berstel, J.: Transductions and Context-Free Languages. Teubner, 1979.

    Google Scholar 

  2. Ginsburg, S.: Algebraic and Automata-Theoretic Properties of Formal Languages. North-Holland, 1975.

    Google Scholar 

  3. Goldstern, M.: Vervollständigung von Halbringen. Diplomarbeit, Technische Universität Wien, 1985.

    Google Scholar 

  4. Karner, G.: On limits in complete semirings. Semigroup Forum 45(1992) 148–165.

    Article  MATH  MathSciNet  Google Scholar 

  5. Kuich, W.: The algebraic equivalent of AFL theory. ICALP95, Lect. Notes Comput. Sci. 944(1995) 39–50.

    MathSciNet  Google Scholar 

  6. Kuich, W.: Semirings and formal power series: Their relevance to formal languages and automata theory. In: G. Rozenberg and A. Salomaa, eds., Handbook of Formal Languages. Springer, to appear.

    Google Scholar 

  7. Kuich, W., Salomaa, A.: Semirings, Automata, Languages. EATCS Monographs on Theoretical Computer Science, Vol. 5. Springer, 1986.

    Google Scholar 

  8. Sakarovitch, J.: Kleene's theorem revisited. Lect. Notes Comput. Sci. 281(1987) 39–50.

    MATH  MathSciNet  Google Scholar 

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Christian Freksa Matthias Jantzen Rüdiger Valk

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© 1997 Springer-Verlag Berlin Heidelberg

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Karner, G., Kuich, W. (1997). On abstract families of languages, power series, and elements. In: Freksa, C., Jantzen, M., Valk, R. (eds) Foundations of Computer Science. Lecture Notes in Computer Science, vol 1337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0052080

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  • DOI: https://doi.org/10.1007/BFb0052080

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63746-2

  • Online ISBN: 978-3-540-69640-7

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