Skip to main content
SpringerLink
Log in

Automata, games, and positive monadic theories of trees

  • Session 1 Automata And Formal Languages
  • Conference paper
  • First Online:
Book cover Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 287))

Abstract

The present paper uses a game theoretic approach to make a fine study of the monadic theory of the infinite binary tree. We characterize some natural classes of monadic formulas in terms of alternating automata; in particular we give a hierarchy of automata corresponding to the hierarchy of alternation of quantifiers for weak monadic formulas. These characterizations lead to efficient decision procedures.

This work was supported by the PRC "Mathématiques et Informatique". A first version has been presented at the meeting of this PRC held at Paris in April 1986.

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. J.R. BUCHI, Using determinancy of games to eliminate quantifiers, Lecture Notes in Computer Science, vol. 56, Springer, 1977, pp. 367–378.

    Google Scholar 

  2. J.R. BUCHI, State-strategies for games in F σδ ∩ G δσ , Journal of Symbolic Logic, vol. 48 (1983), pp. 1171–1198.

    Google Scholar 

  3. Y. GUREVICH and L. HARRINGTON, Trees, automata and games, 14th Symposium on Theory of Computing (1982), pp. 60–65.

    Google Scholar 

  4. D.A. MARTIN, Borel determinancy, Annals of Mathematics, vol. 102 (1975), pp. 363–371.

    Google Scholar 

  5. Y.N. MOSCHOVAKIS, Descriptive set theory, North-Holland, 1980.

    Google Scholar 

  6. D.E. MULLER and P.E. SCHUPP, Alternating automata on infinite objects, determinacy and Rabin's theorem, Lecture Notes in Computer Science, vol. 192, Springer, 1985, pp. 100–107.

    Google Scholar 

  7. D.E. MULLER, A. SAOUDI, and P.E. SCHUPP, Alternating automata, the weak monadic theory of the tree, and its complexity, Proceedings ICALP 1986.

    Google Scholar 

  8. M. PARIGOT, Automata as modal operators, preprint.

    Google Scholar 

  9. M.O. RABIN, Decidability of second order theories and automata on infinite trees, Transations A.M.S., vol. 141 (1969), pp. 1–35.

    Google Scholar 

  10. M.O. RABIN, Weakly definable relations and special automata, Mathematical Logic and Foundations of Set Theory, North Holland, 1970, pp. 1–23.

    Google Scholar 

  11. W. THOMAS, A hierarchy of sets of infinite trees

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Equipe de Logique, CNRS UA 753, Université Paris 7, UFR de Mathématiques, 2 place Jussieu, 75251, Paris Cedex 05

    Michel Parigot

Authors
  1. Michel Parigot
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Kesav V. Nori

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Parigot, M. (1987). Automata, games, and positive monadic theories of trees. In: Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1987. Lecture Notes in Computer Science, vol 287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18625-5_41

Download citation

  • DOI: https://doi.org/10.1007/3-540-18625-5_41

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18625-0

  • Online ISBN: 978-3-540-48033-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation