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Monadic second-order logic and linear orderings of finite structures

  • Bruno Courcelle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 933)

Abstract

We consider graphs in which it is possible to specify linear orderings of the sets of vertices, in uniform ways, by MS (i.e., Monadic Second-order) formulas. We also consider classes of graphs ℂ such that for every L\(\subseteq\)ℂ, L is recognizable iff it is MS-definable. Our results concern in particular dependency graphs of partially commutative words.

Keywords

Linear Order Dependency Graph Regular Language Finite Graph Topological Sorting 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    AALBERSBERG I., ROZENBERG G., Theory of traces, Theoret. Comput. Sci. 60(1988)1–82.CrossRefGoogle Scholar
  2. [2]
    AHO A., HOPCROFT J., ULLMAN J., The design and analysis of computer algorithms, Adison-Wesley, 1974.Google Scholar
  3. [3]
    CORI R., METIVIER Y., ZIELONKA W., Asynchronous mappings and asynchronous cellular automata, Information and Computation 106(1993) 159–203.CrossRefGoogle Scholar
  4. [4]
    COURCELLE B., The monadic second-order logic of graphs I: Recognizable sets of finite graphs. Information and Computation 85 (1990) 12–75.CrossRefGoogle Scholar
  5. [5]
    COURCELLE B., The monadic second-order logic of graphs V: On closing the gap beween definability and recorgnizability, Theoret. Comput. Sci. 80 (1991) 153–202.CrossRefGoogle Scholar
  6. [6]
    COURCELLE B., The monadic second-order logic of graphs VI: On several representations of graphs by relational structures, Discrete Applied Mathematics, 54 (1994)117–149.CrossRefGoogle Scholar
  7. [7]
    COURCELLE B., The monadic second-order logic of graphs VIII: Orientations, Annals Pure Applied Logic, 72(2)(1995).Google Scholar
  8. [8]
    COURCELLE B., The monadic second-order logic of graphs X: Linear orderings, http://www.labri.u-bordeaux.fr/∼courcell/ActSci.html, May 1994Google Scholar
  9. [9]
    COURCELLE B., Monadic second-order definable graph transductions: a survey, Theoret. Comput. Sci. 126(1994) 53–75.CrossRefMathSciNetGoogle Scholar
  10. [10]
    COURCELLE B., Recognizable sets of graphs: equivalent definitions and closure properties, Math. Str. Comp. Sci. 4(1994) 1–32.Google Scholar
  11. [11]
    HOOGEBOOM H., ten PAS P., Recognizable text languages, MFCS 1994, LNCS 841 (1994)413–422.Google Scholar
  12. [12]
    OCHMANSKI E., Regular behaviour of concurrent systems, Bull. of EATCS 27(1985) 56–67.Google Scholar
  13. [13]
    PROSKUROWSKI A., Separating subgraphs in κ-trees: cables and caterpillars, Discrete Maths 49 (1984) 275–285.Google Scholar
  14. [14]
    THOMAS W., Automata on infinite objects, in “Handbook of Theoretical Computer Science, Volume B”, J. Van Leeuwen ed., Elsevier, 1990, pp.133–192.Google Scholar
  15. [15]
    THOMAS W., On logical definability of trace languages, Proce-edings of a workshop held in Kochel in October 1989, V. Diekert ed., Report of Technische Universität München I-9002, 1990, pp. 172–182.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Bruno Courcelle
    • 1
  1. 1.LaBRIUniversité Bordeaux-ITalence CedexFrance

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