Skip to main content
SpringerLink
Log in

Monadic second order logic, tree automata and forbidden minors

  • Conference paper
  • First Online:
Computer Science Logic (CSL 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 533))

Included in the following conference series:

Abstract

N.Robertson and P.D.Seymour proved that each minor closed class K of graphs is characterized by finitely many minimal forbidden minors. If these minors are given then they can be used to find an efficient membership test for such classes (see [Rob Sey 86b]). From these minors one can get a monadic second order description of the class K. Main result of the article is that from a monadic second order description of the class K. Main result of the article is that from a monadic second order description of K the minimal forbidden minors can be constructed, when K contains only graphs of universally bounded tree width. The result is applied to the class of partial 2-pathes.

The research to this article was started in summer 1989 while the first and the third author were visiting the University of Oregon in Eugene. The third author gratefully announces support from the Universities of Toronto, Idaho (Moscow), the Washington State University (Pullmann) and the University of Oregon (Eugene).

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. M.R. Fellows and K. Abrahamson 1989, Cutset-Regularity Beats Well-Quasi-Ordering for Bounded Tree-width (Extended Abstract), preprint Nov. 1989.

    Google Scholar 

  2. S. Arnborg, A. Proskurowski and D.G. Corneil 1986, Forbidden minor characterization of partial 3-trees, Discrete Math., to appear.

    Google Scholar 

  3. S.Arnborg, B.Courcelle, A. Proskurowski and D. Seese 1990, An algebraic theory of graph reduction, preprint January 17, 1990.

    Google Scholar 

  4. S. Arnborg and J. Lagergren 1990, Finding minimal forbidden minors using a finite congruence, preprint November 13, 1990.

    Google Scholar 

  5. S. Arnborg, J. Lagergren and D. Seese 1988, Problems Easy for Tree-descomosable graphs (extended abstract). Proc. 15th ICALP, Springer Verlag, Lect. Notes in Comp. Sc. 317 38–51.

    Google Scholar 

  6. S. Arnborg, J. Lagergren and D. Seese 1989, Problems Easy for Tree-descomposable graphs to appear in J. of Algorithm.

    Google Scholar 

  7. S. Arnborg and A. Proskurowski 1986, Characterization and Recognition of Partial 3-trees, SIAM J.Alg. and Discr. Methods 7, 305–314.

    Google Scholar 

  8. S. Arnborg and A. Proskurowski 1989, Linear Time Algorithm for NP-hard Problems on Graphs Embedded in k-trees Discr. Appl. Math. 23, 11–24.

    Article  Google Scholar 

  9. S. Arnborg, A. Proskurowski, and D. Seese 1989, Logical description of graphs of path-width 2 and their minimal forbidden minors (Draft), preliminary version, preprint July 25, 1989.

    Google Scholar 

  10. H.L. Bodlaender 1887, Dynamic Programming on Graphs with Bounded Tree-width, MIT/LCS/TR-394, MIT.

    Google Scholar 

  11. H.L. Bodlaender 1988, Improved self-reduction algorithms for graphs with bounded tree-width, Technical Report RUU-CS-88-29, September 1988, University of Utrecht.

    Google Scholar 

  12. H.L. Bodlaender, T. KloksBetter Algorithms for the Pathwidth and Treewidth of Graphs (extended abstract), preprint 1990.

    Google Scholar 

  13. J.A. Bondy and U.S.R. Murty 1976, Graph Theory with Applications, North Holland.

    Google Scholar 

  14. B. Courcelle 1988, The monadic second order logic of graphs III: Tree-width, forbidden minors, and complexity issues, Report I — 8852, Bordeaux-1 University.

    Google Scholar 

  15. J.E. Doner 1966, Decidability of the Weak Second Order Theory of two Successors, Abstract 65T-468, Notices Amer. Math. Soc. 12, 819,ibid., 513.

    Google Scholar 

  16. M. Fellows 1989, Nonconstructive Proofs of Polynomial-Time Complexity: Algorithms for Computing Obstructing Sets, draft, preprint April 12, 1989.

    Google Scholar 

  17. M. Fellows 1989, Applications of an Analogue of the Myhill-Nerode Theorem, In Obstruction Set Computation, preprint April 28, 1989.

    Google Scholar 

  18. M. Fellows and M. Langston 1987, Nonconstructive Advances in Polynomial Time Complexity, Info. Proc. Letters 26, 157–162.

    Article  Google Scholar 

  19. M. Fellows and M. Langston 1989, An Analogue of the Myhill-Nerode Theorem and Its Use in Computing Finite-Basis Characterizations (Extended Abstract), to appear, FOCS 89.

    Google Scholar 

  20. M. Fellows and M.Langston 1989, Exploiting RS Posets: Constructive Algorithms from Nonconstructive Tools, preprint revised February 1989.

    Google Scholar 

  21. N.Kinnersley 1989, Obstruction set isolation for layout permutation problems, Ph.D. thesis, Washington State University.

    Google Scholar 

  22. J. Matoušek, R. ThomasAlgorithms finding tree — decompositions of graphs, preprint 1988.

    Google Scholar 

  23. A. Proskurowski 1984, Separating subgraphs in k-trees: cables and caterpillar, Discrete Mathematics 49, 275–285.

    Article  Google Scholar 

  24. M.O. Rabin 1964, A simple Method of Undecidability proofs and some applications, in Log. Meth. Phil. Sci. Proc. Jerusalem, 58–68.

    Google Scholar 

  25. M.O. Rabin 1969, Desidability of second order and automata on infinite trees, Trans. Am. Math. Soc. 141, 1–35.

    Google Scholar 

  26. N. Robertson and P.D. Seymour 1983, Graph Minors I. Excluding a forest, J. Combin. Theory Ser.B. 35, 39–61.

    Google Scholar 

  27. N. Robertson and P.D. Seymour 1986 Graph Minors II. Algorithmic Aspects of Tree Width Journal of Algorithms, 7, 309–322.

    Article  Google Scholar 

  28. N. Robertson and P.D. Seymour 1986, Graph Minors V. Excluding a planar graph J. Combinatorial Theory, Ser. B, 41, 92–114.

    Google Scholar 

  29. N. Robertson and P.D. Seymour 1986, Graph Minors XIII. The Disjoint Path Problem Preprint.

    Google Scholar 

  30. N. Robertson and P.D. Seymour 1988, Graph Minors XV. Wagners conjecture Preprint.

    Google Scholar 

  31. N. Robertson and P.D. Seymour 1989, Personal Communication, Toronto, Eugene.

    Google Scholar 

  32. P. Scheffler 1986, Dynamic programming algorithms for tree-descomposition problems, Karl-Weierstrass-Institut für Mathematik, Preprint P-Math-28/86, Berlin.

    Google Scholar 

  33. P. Scheffler 1989 Die Baumwerte von Graphen als ein Maß für die Kompliziertheit algorithmischer Probleme, Dissertation (A), AdW d. DDR, Berlin 1989.

    Google Scholar 

  34. D. Seese 1985, Tree-partite graphs and the complexity of algorithms (extended abstract), in FCT'85, ed. L. Budach, LNCS 199, Springer, Berlin, 412–421.

    Google Scholar 

  35. D. Seese 1986, Tree-partite graphs and the complexity of algorithms, preprint P-Math 08/86, Karl-Weierstrass-Institute für Mathematik.

    Google Scholar 

  36. J.W. Thatcher and J.B. Wright 1968, Generalized Finite Automata Theory with an Application to a Decision Problem in Second-Order Logic, Mathematical Systems Theory 2, 57–81.

    Google Scholar 

  37. T.V. Wimer 1988, Ph D Thesis URI-030, Clemson.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. NADA,KTH, S-100 44, Stockholm, Sweden

    Stefan Arnborg

  2. Department of Computer and Information Science, University of Oregon, 97403, Eugène, Oregon, USA

    Andrzej Proskurowski

  3. Karl-Weierstrass Institute for Mathematics, Mohrenstr. 39, PF 1304, O-1086, Berlin, Germany

    Detlef Seese

Authors
  1. Stefan Arnborg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrzej Proskurowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Detlef Seese
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Egon Börger Hans Kleine Büning Michael M. Richter Wolfgang Schönfeld

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Arnborg, S., Proskurowski, A., Seese, D. (1991). Monadic second order logic, tree automata and forbidden minors. In: Börger, E., Kleine Büning, H., Richter, M.M., Schönfeld, W. (eds) Computer Science Logic. CSL 1990. Lecture Notes in Computer Science, vol 533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54487-9_49

Download citation

  • DOI: https://doi.org/10.1007/3-540-54487-9_49

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54487-6

  • Online ISBN: 978-3-540-38401-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation