Nothing Special   »   [go: up one dir, main page]

Skip to main content

The Wadge-Wagner hierarchy of ω-rational sets

  • Invited Papers
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1256))

Included in the following conference series:

Abstract

We present a unified treatment of the hierarchy defined by Klaus Wagner for ω-rational sets and also introduced in the more general framework of descriptive set theory by William W. Wadge. We show that this hierarchy can be defined by syntactic invariants, using the concept of an ω-semigroup.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Jorge Almeida. Finite Semigroups and Universal Algebra. World Scientific, 1994.

    Google Scholar 

  2. Rana Barua. The Hausdorff-Kuratowski hierarchy of ω-regular languages and a hierarchy of Muller automata. Theoretical Computer Science, 96:345–360, 1992.

    Article  Google Scholar 

  3. Nicolas Bedon. Automata, semigroups and recognizability of words on ordinals. IGM report 96-5, to appear in International Journal of Algebra and Computation.

    Google Scholar 

  4. Olivier Carton. Mots infinis, ω-semigroupes et Topologie. Thèse, Université Paris 7, 1993. Report LITP-TH 93-08.

    Google Scholar 

  5. Olivier Carton and Dominique Perrin. The Wagner hierarchy of ω-rational sets. To appear in International journal of algebra and computation.

    Google Scholar 

  6. Olivier Carton and Dominique Perrin. Chains and superchains in ω-semigroups. In Jorge Almeida, Grancinda Gomes, and Pedro Silva, editors, Semigroups, Automata and Languages, pages 17–28. World Scientific, 1994.

    Google Scholar 

  7. Olivier Carton and Dominique Perrin. Chains and superchains for ω-rational sets, automata and semigroups. International journal of algebra and computation, 1997. to appear.

    Google Scholar 

  8. John M. Howie. Fundamentals of Semigroup Theory. Oxford University Press, 1995.

    Google Scholar 

  9. Micheal Kaminski. A classification of ω-regular languages. Theoretical Computer Science, 36:217–229, 1985.

    Article  Google Scholar 

  10. Alexander S. Kechris. Classical Descriptive Set Theory, volume 156 of Graduate texts in mathematics. 1995.

    Google Scholar 

  11. Sriram C. Krishnan, Anuj Puri, and Robert K. Brayton. Structural complexity of ω-languages. In STACS '95, volume 900 of Lecture Notes in Computer Science, pages 143–156, Berlin, 1995. Springer-Verlag.

    Google Scholar 

  12. Lawrence H. Landweber. Decision problems for ω-automata. Mathematical Systems Theory, 3:376–384, 1969.

    Article  Google Scholar 

  13. Douglas Lind and Brian Marcus. An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, 1995.

    Google Scholar 

  14. Alain Louveau. Some results in the Wadge hierarchy of Borel sets. In A.S. Kechris et al., editor, Cabal Seminar 79-81, volume 1019 of Lecture Notes in Math., pages 28–55. Springer-Verlag, 1981.

    Google Scholar 

  15. Zohar Manna and Amir Pnueli. A hierarchy of temporal properties. In Principles of Distributed Computing, pages 377–408, 1990.

    Google Scholar 

  16. Dominique Perrin and Jean-Eric Pin. Infinite words. Version 1.4, Report LITP 97.04 (http://litp.ibp.fr/∼jep/Resumes/MotsInfinis.html).

    Google Scholar 

  17. Dominique Perrin and Jean-Eric Pin. Semigroups and automata on infinite words. In J. Fountain and V. A. R. Gould, editors, NATO Advanced Study Institute Semi-groups, Formal Languages and Groups, pages 49–72. Kluwer academic publishers, 1995.

    Google Scholar 

  18. Jean-Eric Pin. A variety theorem without complementation. Russian Mathematics (Iz. VUZ), 39:80–90, 1995.

    Google Scholar 

  19. Pierre Simonnet. Automates et Théorie Descriptive. Thèse, Université Paris 7, 1992.

    Google Scholar 

  20. Ludwig Staiger and Klaus Wagner. Automatentheoretische und automatenfreie Charakterisierungen topologischer Klassen regulärer Folgenmengen. Elektron. Informationsverarb. Kybernet., 10:379–392, 1974.

    Google Scholar 

  21. Wolfgang Thomas. Automata on infinite objects. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B, chapter 4. Eisevier, 1990.

    Google Scholar 

  22. Klaus Wagner. On ω-regular sets. Information and Control, 43:123–177, 1979.

    Article  Google Scholar 

  23. Thomas Wilke. An Eilenberg theorem for ∞-languages. In ICALP '91, volume 510 of Lecture Notes in Computer Science, pages 588–599, Berlin, 1991. Springer-Verlag.

    Google Scholar 

  24. Thomas Wilke. An algebraic theory for regular languages of finite and infinite words. Int. J. Alg. Comput., 3(4):447–489, 1993.

    Article  Google Scholar 

  25. Thomas Wilke and Haiseung Yoo. Computing the Rabin index of a regular language of infinite words. To appear in International Journal of Algebra and Computation, 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Pierpaolo Degano Roberto Gorrieri Alberto Marchetti-Spaccamela

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Carton, O., Perrin, D. (1997). The Wadge-Wagner hierarchy of ω-rational sets. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_162

Download citation

  • DOI: https://doi.org/10.1007/3-540-63165-8_162

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63165-1

  • Online ISBN: 978-3-540-69194-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics