Graphs as relational structures : An algebraic and logical approach

  • Bruno Courcelle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 532)


Relational structures form a unique framework in which various types of graphs and hypergraphs can be formalized and studied. We define operations on structures that are compatible with monadic second-order logic, and that are powerful enough to represent context-free graph- and hypergraph-grammars of various types, namely, hyperedge replacement, C-edNCE, and separated handle replacement ones. Several results on monadic second-order properties of the generated sets are obtained in a uniform way.


Context-free graph-grammar C-edNCE graph-grammar Graphs Graph operation Hypergraph Hyperedge replacement Monadic second-order logic Monadic second-order definable graph transformation Relational structure 


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  1. [1]
    BAUDERON M., COURCELLE B., Graph expressions and graph rewritings, Mathematical System Theory 20 (1987) 83–127.CrossRefGoogle Scholar
  2. [2]
    COURCELLE B., Equivalences and transformations of regular systems. Applications to recursive program schemes and grammars, Theor. Comp. Sci. 42 (1986), 1–122.CrossRefGoogle Scholar
  3. [3]
    COURCELLE B., A representation of graphs by algebraic expressions and its use for graph rewriting systems, Proceedings of the 3rd International Workshop on Graph Grammars, L.N.C.S. 291, Springer, 1987, pp. 112–132.Google Scholar
  4. [4]
    COURCELLE B., On context-free sets of graphs and their monadic second-order theory, same volume as [3], pp. 133–146.Google Scholar
  5. [5]
    COURCELLE B., An axiomatic definition of context-free rewriting and its application to NLC graph grammars, Theoretical Computer Science 55 (1987) 141–181.CrossRefGoogle Scholar
  6. [6]
    COURCELLE B., Graph rewriting: An algebraic and logic approach, in "Handbook of Theoretical Computer Science,Volume B", J. Van Leeuwen ed., Elsevier,1990, pp.193–242Google Scholar
  7. [7]
    COURCELLE B., The monadic second-order logic of graphs I, recognizable sets of finite graphs. Information and Computation 85 (1990) 12–75.CrossRefGoogle Scholar
  8. [8]
    COURCELLE B., The monadic second-order logic of graphs V: On closing the gap between definability and recognizability, Research Report 89–91, Bordeaux I University, to appear in Theor. Comput. Sci.Google Scholar
  9. [9]
    COURCELLE B., The monadic second order logic of graphs VI: On several representations of graphs by relational structures, Report 89-99, (see also Logic in Computer Science 1990, Philadelphia).Google Scholar
  10. [10]
    COURCELLE B., The monadic second-order logic of graphs VII: Graphs as relational structures, in preparation.Google Scholar
  11. [11]
    COURCELLE B., ENGELFRIET J., A logical characterization of hypergraph languages generated by hyperedge replacement grammars, in preparation.Google Scholar
  12. [12]
    COURCELLE B., ENGELFRIET J., ROZENBERG G., Handle-rewriting hypergraph grammars, this volume.(Long version as research report 90-84, Bordeaux-I University, or reports 90-08 and 90-09 of the University of Leiden).Google Scholar
  13. [13]
    EHRIG H. et al., Transformations of structures, an algebraic approach, Math. Systems Theory 14 (1981) 305–334.CrossRefGoogle Scholar
  14. [14]
    ENGELFRIET J., A characterization of context-free NCE graph languages by monadic-second order logic on trees, preprint, 1990.Google Scholar
  15. [15]
    ENGELFRIET J., ROZENBERG G., A comparison of boundary graph grammars and context-free hypergraph grammars,Information and Computation 84 (1990) 163–206.CrossRefGoogle Scholar
  16. [16]
    HABEL A., KREOWSKI H.J., May we introduce to you: Hyperedge replacement, same volume as [3], pp. 15–26.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Bruno Courcelle
    • 1
  1. 1.Laboratoire d'InformatiqueUniversité Bordeaux-ITalence - CedexFrance

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