Skip to main content
SpringerLink
Log in

The kleene and the Parikh Theorem in complete semirings

  • Formal Languages And Automata
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 267))

Included in the following conference series:

Abstract

The Kleene and the Parikh Theorem are generalized to complete semirings with the additional property that limits can be defined by infinite sums.

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. Carré, B.: Graphs and Networks, Clarendon Press (1979).

    Google Scholar 

  2. Eilenberg, S.: Automata, Languages and Machines, Vol.A., Academic Press (1974).

    Google Scholar 

  3. Eilenberg, S. and Schützenberger, M.P.: Rational Sets in commutative monoids, J.Algebra 13(1969), 173–191.

    Article  Google Scholar 

  4. Goldstern, M.: Vervollständigung von Halbringen, Diplomarbeit Technische Universität Wien (1985).

    Google Scholar 

  5. Kuich,W. and Salomaa,A.: Semirings, Automata, Languages, Springer (1986).

    Google Scholar 

  6. Küster, G.: Das Hadamardprodukt Abstrakter Familien von Potenzreihen, Dissertation Technische Universität Wien (1987).

    Google Scholar 

  7. Mahr, B.: Semirings and transitive closure, Bericht Nr. 82–5, Fachbereich Informatik, TU Berlin (1982).

    Google Scholar 

  8. Pilling, D.L.: Commutative regular equations and Parikh's Theorem, J.London Math.Soc.,II.Ser. 6, 663–666 (1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Werner Kuich

Authors
  1. Werner Kuich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Thomas Ottmann

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kuich, W. (1987). The kleene and the Parikh Theorem in complete semirings. In: Ottmann, T. (eds) Automata, Languages and Programming. ICALP 1987. Lecture Notes in Computer Science, vol 267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18088-5_17

Download citation

  • DOI: https://doi.org/10.1007/3-540-18088-5_17

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18088-3

  • Online ISBN: 978-3-540-47747-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation