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On context-free sets of graphs and their monadic second-order theory

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Graph-Grammars and Their Application to Computer Science (Graph Grammars 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 291))

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Abstract

The algebraic framework for studying graphs yields a notion of system of equations defining equational sets of graphs. Context-free graph grammars (where the rewriting step is the substitution a graph for an hyperedge) are defined. The context-free and the equational sets of graphs are the same. The monadic second-order theory of a context-free set of graphs is decidable.

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Note : This work has been supported by the "Projet de Recherches Coordonnées" : " Mathématiques et Informatique" of CNRS.

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References

  1. J.R. BUCHI, Weak 2nd order logic and finite automata, Z. Math Logik 5(960) 66–92.

    Google Scholar 

  2. B. COURCELLE, A representation of graphs by algebraic expressions and its use for graph rewriting systems, this volume.

    Google Scholar 

  3. B. COURCELLE, An axiomatic definition of context-free rewriting and its application to NLC grammars, Report 8706, Bordeaux 1 University, 1987.

    Google Scholar 

  4. J.DONER, Tree acceptors and applications. Jour. Comput. System Sci. 4(70) 406–451

    Google Scholar 

  5. J.W. THATCHER, J.B. WRIGHT, Generalized automata theory, Maths Systems Theory 2 (1970) 57–81

    Article  Google Scholar 

  6. P. SEYMOUR, N. ROBERTSON, Some new results on the well quasiordering of graphs, Annals of Discrete Maths 23 (1984) 343–354.

    Google Scholar 

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Hartmut Ehrig Manfred Nagl Grzegorz Rozenberg Azriel Rosenfeld

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© 1987 Springer-Verlag Berlin Heidelberg

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Courcelle, B. (1987). On context-free sets of graphs and their monadic second-order theory. In: Ehrig, H., Nagl, M., Rozenberg, G., Rosenfeld, A. (eds) Graph-Grammars and Their Application to Computer Science. Graph Grammars 1986. Lecture Notes in Computer Science, vol 291. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18771-5_50

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  • DOI: https://doi.org/10.1007/3-540-18771-5_50

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18771-4

  • Online ISBN: 978-3-540-48178-2

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