Skip to main content
SpringerLink
Log in

Tree automata, tree decomposition and hyperedge replacement

  • Conference paper
  • First Online:
Book cover Graph Grammars and Their Application to Computer Science (Graph Grammars 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 532))

Abstract

Recent results concerning efficient solvability of graph problems on graphs with bounded tree-width and decidability of graph properties for hyperedge-replacement graph grammars are systematised by showing how they can be derived from recognisability of corresponding tree classes by finite tree automata, using only well-known techniques from tree-automata theory.

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, Efficient algorithms for combinatorial problems on graphs with bounded decomposability — a survey. BIT 25 (1985), pp. 2–23.

    Article  Google Scholar 

  2. S. Arnborg, D. Corneil, A. Proskurowski, Complexity of finding embeddings in a k-tree. SIAM J.Alg.Disc.Meth. 8 (1987), pp.277–284.

    Google Scholar 

  3. S.Arnborg, J.Lagergren, D.Seese, Which problems are easy for tree-decomposable graphs? LNCS 317, pp. 38–51.

    Google Scholar 

  4. M. Bauderon, B. Courcelle, A Graph Expressions and graph rewriting. Math. Systems Theory 20 (1987), pp. 83–127.

    Article  Google Scholar 

  5. H.L.Bodlaender, Classes of graphs with bounded tree-width. Report RUU-CS-86-22, Rijksuniversiteit Utrecht, vakgroep informatica, 1986.

    Google Scholar 

  6. H.L.Bodlaender, Dynamic programming on graphs with bounded tree-width. LNCS 317, pp. 105–118.

    Google Scholar 

  7. H.Bodlaender, NC-algorithms for graphs with small treewidth. Report RUU-CS-88-4, Rijsuniversiteit Utrecht, vakgroep informatica, 1988.

    Google Scholar 

  8. H.L.Bodlaender, Planar graphs with bounded tree-width. Report RUU-CS-88-14, Rijksuniversiteit Utrecht, vakgroep informatica, 1988.

    Google Scholar 

  9. S.A. Cook, Towards a complexity theory of synchronous parallel computation. L'Enseignement mathématique 27 (1981), pp. 99–124.

    Google Scholar 

  10. B. Courcelle, An axiomatic definition of context-free rewriting and its application to NLC graph grammars. TCS 55 (1987), pp. 141–181.

    Article  Google Scholar 

  11. B.Courcelle, The monadic second-order logic of graphs, III: Tree-width, forbidden minors, and complexity issues. Preprint, Université Bordeaux 1, 1988.

    Google Scholar 

  12. B. Courcelle, The monadic second-order logic of graphs, I: Recognizable sets of finite graphs. I&C 85 (1990), pp. 12–75.

    Google Scholar 

  13. J.E. Doner, Tree acceptors and some of their applications. JCSS 4 (1970), pp. 406–451.

    Google Scholar 

  14. F. Gécseg, M. Steinby, Tree automata. Akadémiai Kiadó, Budapest 1984.

    Google Scholar 

  15. A. Habel, Hyperedge replacement: Grammars and languages. Dissertation, Bremen 1989.

    Google Scholar 

  16. A. Habel, H.-J. Kreowski, Some structural aspects of hypergraph languages generated by hyperedge replacement. LNCS 247 (1987), pp. 207–219.

    Google Scholar 

  17. A.Habel, H.-J.Kreowski, C.Lautemann, A comparison of compatible, finite, and inductive graph properties. Report No. 7/89, Fachbereich Mathematik/Informatik, Universität Bremen, 1989, to appear in TCS.

    Google Scholar 

  18. A. Habel, H.-J. Kreowski, W. Vogler, Metatheorems for decision problems on hyperedge-replacement graph languages. Acta Informatica 26 (1989), pp. 657–677.

    Article  Google Scholar 

  19. A.Habel, H.-J.Kreowski, W.Vogler, Decidable boundedness problems for sets of graphs generated by hyeredge replacement. To appear in TCS.

    Google Scholar 

  20. J.E.Hopcroft, J.D.Ullman, Introduction to automata theory, languages, and computation. Addison-Wesley, 1979.

    Google Scholar 

  21. D.S. Johnson, The NP-completeness column: An ongoing guide. J. Algorithms 6 (1985), pp. 434–451.

    Article  Google Scholar 

  22. C. Lautemann, Decomposition trees: structured graph representation and efficient algorithms. LNCS 299 (1988), pp. 28–39.

    Google Scholar 

  23. C. Lautemann, Efficient algorithms on context-free graph languages. LNCS 317 (1988), pp. 362–378.

    Google Scholar 

  24. C. Lautemann, The complexity of graph languages generated by hyperedge replacement. Acta Informatica 27, 399–421 (1990)

    Article  Google Scholar 

  25. C.Lautemann, Tree decomposition of graphs and tree automata. Informatik-Bericht 2/90, Johannes-Gutenberg Universität Mainz, 1990.

    Google Scholar 

  26. T.Lengauer, E.Wanke, Efficient analysis of graph properties on context-free graph languages (Extended abstract). LNCS 317, pp. 379–393. Revised version as Report 45 (1989), Fachbereich Mathematik-Informatik, Universität-Gesamthochschule Paderborn.

    Google Scholar 

  27. J.Y.-T. Leung, J. Witthof, O. Vornberger, On some variations of the bandwidth minimization problem. SIAM J. Comp. 13 (1984), pp. 650–667.

    Article  Google Scholar 

  28. N. Robertson, P.D. Seymour, Graph minors. II. Algorithmic aspects of tree-width. J. Algorithms 7 (1986), pp. 309–322.

    Article  Google Scholar 

  29. N.Robertson, P.D.Seymour, Graph minors. XIII. The disjoint paths problem. Preprint 1986.

    Google Scholar 

  30. W.L. Ruzzo, Tree-size bounded alternation. JCSS 20 (1980), pp. 218–235.

    Google Scholar 

  31. J.W.Thatcher, Tree automata: an informal survey. In: “Currents in the theory of computing” (ed. A.V.Aho), Prentice-Hall 1973, pp.143–172.

    Google Scholar 

  32. J.W. Thatcher, J.B. Wright, Generalized finite automata theory with an application to a decision problem of second-order logic. Math. Syst. Theory 2 (1968), pp. 57–81

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Johannes Gutenberg Universität, D-6500, Mainz

    Clemens Lautemann

Authors
  1. Clemens Lautemann
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Hartmut Ehrig Hans-Jörg Kreowski Grzegorz Rozenberg

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lautemann, C. (1991). Tree automata, tree decomposition and hyperedge replacement. In: Ehrig, H., Kreowski, HJ., Rozenberg, G. (eds) Graph Grammars and Their Application to Computer Science. Graph Grammars 1990. Lecture Notes in Computer Science, vol 532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017410

Download citation

  • DOI: https://doi.org/10.1007/BFb0017410

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54478-4

  • Online ISBN: 978-3-540-38395-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation