Hostname: page-component-7bb8b95d7b-lvwk9 Total loading time: 0 Render date: 2024-09-22T09:37:23.194Z Has data issue: false hasContentIssue false
  • English
  • Français

Equivalent definitions of recognizability for sets of graphs of bounded tree-width

Published online by Cambridge University Press:  04 March 2009

Bruno Courcelle  and
Jens Lagergren
Bruno Courcelle
Affiliation:
Université Bordeaux-1, LaBRI, 351 cours de la Libération, 33405 Talence, France Email courcell@labri.u-bordeaux.fr
Jens Lagergren
Affiliation:
Department of Numerical Analysis and Computing Science, The Royal Institute of Technology, S-100 44 Stockholm, Sweden Email jensl@nada.kth.se
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that a set of finite graphs of tree-width at most k is recognizable (with respect to the algebra of graphs with an unbounded number of sources) if and only if it is recognizable with respect to the algebra of graphs of tree-width at most k with at most k sources.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 6 , Issue 2 , April 1996 , pp. 141 - 165
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abrahamson, K. and Fellows, M. (1993) Finite automata, bounded tree-width and well-quasiordering. In: Robertson, N. and Seymour, P. (eds.) Graph Structure Theory. Contemporary Mathematics 147 539–564.CrossRefGoogle Scholar
Arnborg, S., Courcelle, B., Proskurowski, A. and Seese, D. (1993) An algebraic theory of graph reduction. Journal of ACM 40 (5) 1134–1164.CrossRefGoogle Scholar
Arnborg, S., Lagergren, J. and Seese, D. (1991) Problems easy for tree-decomposable graphs. Journal of Algorithms 12 308–340.CrossRefGoogle Scholar
Courcelle, B. (1990) The monadic second order logic of graphs I: Recognizable sets of finite graphs. Information and Computation 85 12–75.CrossRefGoogle Scholar
Courcelle, B. (1992) The monadic second-order logic of graphs III: Tree-decompositions, minors and complexity issues. Informatique Théorique et Applications 26 257–286.CrossRefGoogle Scholar
Courcelle, B. (1994) Recognizable sets of graphs: equivalent definitions and closure properties. Mathematical Structures in Computer Science 4 1–32.CrossRefGoogle Scholar
Courcelle, B. and Lagergren, J. (1994) Recognizable sets of graphs of bounded tree-width. In: Proceedings of a Dagsthul Seminar on Graph grammars held in 1993. Springer-Verlag Lecture Notes in Computer Science 776 138–152.CrossRefGoogle Scholar
Engelfriet, J. (1994) Tree transductions and graph grammars. In: Proceedings CAAP 94. Springer-Verlag Lecture Notes in Computer Science 787 15–36.CrossRefGoogle Scholar
Habel, A. (1992) Hyperedge replacement: grammars and languages. Springer-Verlag Lecture Notes in Computer Science 643.Google Scholar
Habel, A., Kreowski, H. J. and Lautemann, C. (1991) A comparison of compatible, finite, and inductive graph properties. Theoretical Computer Science 89 33–62.CrossRefGoogle Scholar
Lagergren, J. and Arnborg, S. (1991) Finding minimal forbidden minors using a finite congruence. In: Proceedings 18th ICALP. Springer-Verlag Lecture Notes in Computer Science 510 532–543.CrossRefGoogle Scholar
Mezei, J. and Wright, J. (1967) Algebraic automata and context-free sets. Information and Control 11 3–29.CrossRefGoogle Scholar