Skip to main content

Locally threshold testable languages of infinite words

  • Conference paper
  • First Online:
STACS 93 (STACS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 665))

Included in the following conference series:

  • 149 Accesses

Abstract

The class of finitely locally threshold testable ω-languages is proved to be decidable relatively to the class of all regular ω-languages. We apply this to the monadic second order theory of infinite word structures with successor function: it is decidable whether for a given monadic second-order formula there exists a first-order formula with the same set of infinite word models.

Supported by ESPRIT Basic Research Action Working Group No. 3166 ‘Algebraic and Syntactic Methods in Computer Science’ (ASMICS).

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. Claude Berge, Graphs, second revised ed., North-Holland Mathematical Library, vol. 6, North-Holland, Amsterdam, 1985, part 1.

    Google Scholar 

  2. Daniele Beauquier and Jean Eric Pin, Factors of words, Automata, Languages and Programming: 16th Intern. Coll., Stresa, 1989, Proc. (G. Ausiello, M. Dezani-Ciancaglini, and S. Ronchi Della Rocca, eds.), Lecture Notes in Computer Science, vol. 372, Springer, 1989, pp 63–79.

    Google Scholar 

  3. Janus A. Brzozowski and Imre Simon, Characterization of locally testable events, Discrete Math. 4 (1973), 243–271.

    Google Scholar 

  4. J. Richard Büchi, On a decision method in restricted second-order arithmetic, Logic, Methodology, and Philosophy of Science: Proc of the 1960 International Congress (E. Nagel, P. Suppes, and A. Tarski, eds.), Stanford University Press, 1962, pp 1–11.

    Google Scholar 

  5. Laurence H. Landweber, Decision problems for ω-automata, Math. Systems Theory 3 (1969), 376–384.

    Google Scholar 

  6. Robert McNaughton, Algebraic decision procedures for local testability, Math. Systems Theory 8 (1974), 60–76.

    Google Scholar 

  7. Ludwig Staiger and Klaus Wagner, Automatentheoretische Charakterisierungen topologischer Klassen regulärer Folgenmengen, Elektron. Informationsverarb. Kybernet. 10 (1974), 379–392.

    Google Scholar 

  8. Wolfgang Thomas, Classifying regular events in symbolic logic, J. Comput. System Sci. 25 (1982), 360–376.

    Google Scholar 

  9. Wolfgang Thomas, Automata on infinite objects, Handbook of Theoretical Computer Science (Jan van Leeuwen, ed.), Elsevier Science Publishers B.V., 1990, pp 134–191.

    Google Scholar 

  10. Thomas Wilke, An algebraic theory for regular languages of finite and infinite words, Technical report 9202, Inst f. Inform. u. Prakt. Math., Univ. Kiel, Germany, 1992. To appear in Intern. J. Algebra Comput.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

P. Enjalbert A. Finkel K. W. Wagner

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wilke, T. (1993). Locally threshold testable languages of infinite words. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_60

Download citation

  • DOI: https://doi.org/10.1007/3-540-56503-5_60

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56503-1

  • Online ISBN: 978-3-540-47574-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics