Skip to main content
SpringerLink
Log in

A hierarchical approach to monadic second-order logic over graphs

  • Conference paper
  • First Online:
Computer Science Logic (CSL 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1414))

Included in the following conference series:

  • 123 Accesses

Abstract

The expressiveness of existential monadic second-order logic is investigated over several classes of finite graphs among them the graphs of bounded tree-width. A hierarchical approach to the decomposition of graphs is introduced which is related to the notion of tree decomposition. Among other results we show that existential monadic second-order logic on graphs of bounded tree-width is not closed under complement.

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. S. Arnborg, J. Lagergren, D. Seese, Easy problems for tree-decomposible graphs, J. of Algorithms 12 (1991), 308–340.

    Article  Google Scholar 

  2. B. Courcelle, The monadic second-order logic of graphs, II: Infinite graphs of bounded width, Math. Systems Theory 21 (1989), 187–221.

    Article  Google Scholar 

  3. D. Giammarresi, A. Restivo, S. Seibert, W. Thomas, Monadic second-order logic over rectangular pictures and recognizability by tiling systems, Information and Computation 125 (1996), 32–45.

    Article  Google Scholar 

  4. R. Fagin, Monadic generalized spectra. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 98 (1975), 89–96.

    Google Scholar 

  5. A. Potthoff, S. Seibert, W. Thomas, Nondeterminism versus determinism of finite automata over acyclic directed graphs, Bull. Belg. Math. Soc. Simon Stevin 1 (1994), 285–298.

    Google Scholar 

  6. N. Robertson, P.D. Seymour, Graph minors I. Excluding a forest, J. of Combinatorial Theory, Series B 39 (1983), 39–61.

    Google Scholar 

  7. I. Schiering, Doctoral Dissertation, University of Kiel (in preparation).

    Google Scholar 

  8. D. Seese, The structure of the models of decidable monadic theories of graphs, Annals of Pure and Applied Logic 53 (1991), 169–195.

    Article  Google Scholar 

  9. D. Seese, Interpretability and tree automata: a simple way to solve algorithmic problems on graphs closely related to trees, in: Tree Automata and Languages (M. Nivat, A. Podelski Eds.), Elsevier Science Publishers, 1992, pp. 83–114.

    Google Scholar 

  10. W. Thomas, On logics tilings, and automata, in Automata, Languages, and Programming (J. Leach et al., Eds.), Lecture Notes in Computer Science 510, Springer-Verlag, Berlin 1991, pp. 441–453.

    Google Scholar 

  11. W. Thomas, Elements of an automata theory over partial orders, in: Partial Order Methods in Verification (D.A. Peled et al., eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science Vol. 29, Amer. Math. Soc. 1997, pp. 25–40.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Universität Kiel, D-24098, Kiel

    Ina Schiering

Authors
  1. Ina Schiering
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Mogens Nielsen Wolfgang Thomas

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Schiering, I. (1998). A hierarchical approach to monadic second-order logic over graphs. In: Nielsen, M., Thomas, W. (eds) Computer Science Logic. CSL 1997. Lecture Notes in Computer Science, vol 1414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028029

Download citation

  • DOI: https://doi.org/10.1007/BFb0028029

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64570-2

  • Online ISBN: 978-3-540-69353-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation