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Context-free graph grammars: Separating vertex replacement from hyperedge replacement

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Fundamentals of Computation Theory (FCT 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 710))

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Abstract

We establish that a set of graphs generated by a “Vertex replacement” graph grammar can be generated by a “Hyperedge replacement” one iff its graphs do not contain arbitrarily large complete bipartite graphs Kn,n as subgraphs, iff its graphs have a number of edges that is linearly bounded in terms of the number of vertices. These properties are decidable by means of an appropriate extension of the theorem by Parikh that characterizes the commutative images of context-free languages.

Supported by the ESPRIT Basic Research Working Group “COMPUGRAPH II” (“Computing by graph transformation”).

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L.N.C.S. means Lecture Notes in Computer Science, Springer Verlag, Heidelberg, Berlin, New-York.

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Authors and Affiliations

  1. Bordeaux-I University, France

    Bruno Courcelle

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  1. Bruno Courcelle
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Correspondence to Bruno Courcelle .

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Zoltán Ésik

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© 1993 Springer-Verlag Berlin Heidelberg

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Courcelle, B. (1993). Context-free graph grammars: Separating vertex replacement from hyperedge replacement. In: Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 1993. Lecture Notes in Computer Science, vol 710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57163-9_14

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  • DOI: https://doi.org/10.1007/3-540-57163-9_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57163-6

  • Online ISBN: 978-3-540-47923-9

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