Skip to main content
SpringerLink
Log in

Gaußian elimination and a characterization of algebraic power series

  • Contributed Papers
  • Conference paper
  • First Online:
Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

We show first how systems of equations can be solved by Gaußian elimination. This yields a characterization of algebraic power series and of \(\mathfrak{A}\mathfrak{l}\mathfrak{g}(A'),{\mathbf{ }}A'{\mathbf{ }} \subseteq {\mathbf{ }}A\), A a continuous semiring. In the case of context-free languages this characterization coincides with the characterization given by Gruska [7].

Supported by Stiftung Aktion österreich-Ungarn

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Autebert, J.-M., Berstel, J., Boasson, L.: Context-free languages and pushdown automata. In: Handbook of Formal Languages (Eds.: G. Rozenberg and A. Salomaa), Springer, 1997, Vol. 1, Chapter 3, 111–174.

    Google Scholar 

  2. Bekic, H.: Definable operations in general algebras, and the theory of automata and flowcharts. Tech. Report, IBM Labor, Wien, 1967.

    Google Scholar 

  3. Bozapalidis, S.: Equational elements in additive algebras. Technical Report, Aristotle University of Thessaloniki, 1997.

    Google Scholar 

  4. Esik, Z.: Completeness of Park induction. Theor. Comput. Sci. 177(1997) 217–283.

    Article  MATH  MathSciNet  Google Scholar 

  5. Gecseg, F., Steinby, M.: Tree Languages. In: Handbook of Formal Languages (Eds.: G. Rozenberg and A. Salomaa), Springer, 1997, Vol. 3, Chapter 1, 1–68.

    Google Scholar 

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

    Google Scholar 

  7. Gruska, J.: A characterization of context-free languages. Journal of Computer and System Sciences 5(1971) 353–364.

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  9. Kuich, W.: The Kleene and the Parikh theorem in complete semirings. ICALP87, Lect. Notes Comput. Sci. 267(1987) 212–225.

    MATH  MathSciNet  Google Scholar 

  10. Kuich, W.: Semirings and formal power series: Their relevance to formal languages and automata theory. In: Handbook of Formal Languages (Eds.: G. Rozenberg and A. Salomaa), Springer, 1997, Vol. 1, Chapter 9, 609–677.

    Google Scholar 

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

    Google Scholar 

  12. Lausch, H., Nöbauer, W.: Algebra of Polynomials. North-Holland, 1973.

    Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  14. Salomaa, A.: Formal Languages. Academic Press, 1973.

    Google Scholar 

  15. Thatcher, J. W., Wright, J. B.: Generalized finite automata theory with an application to a decision problem of second-order logic. Math. Systems Theory 2(1968) 57–81.

    Article  MATH  MathSciNet  Google Scholar 

  16. Wechler, W.: Universal Algebra for Computer Scientists. EATCS Monographs on Computer Science, Vol. 25. Springer, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Abteilung für Theoretische Informatik Institut für Algebra und Diskrete Mathematik, Technische Universität Wien, österreich

    Werner Kuich

Authors
  1. Werner Kuich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Luboš Brim Jozef Gruska Jiří Zlatuška

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kuich, W. (1998). Gaußian elimination and a characterization of algebraic power series. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055801

Download citation

  • DOI: https://doi.org/10.1007/BFb0055801

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation