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Recognizing edge replacement graph languages in cubic time

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Book cover Graph Grammars and Their Application to Computer Science (Graph Grammars 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 532))

Abstract

While in general the recognition problem for (hyper-)edge replacement grammars is NP-complete, there are polynomial algorithms for restricted graph classes. The degree of the corresponding polynomial depends on the size of the right hand sides of the grammar, and this size cannot be restricted without restricting the generative power.

In this paper we show that for the class of cyclically connected graphs the recognition problem for edge replacement grammars can be solved in cubic time, i.e. the degree of the polynomial does not depend on the size of the right hand sides of the grammar. For this result we give a suitable normal form for an edge replacement grammar. The algorithm uses the idea of the Cocke-Kasami-Younger algorithm and depends crucially on an algorithm of Hopcroft and Tarjan, which can be used to determine the form of a derivation tree for the given graph.

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Authors and Affiliations

  1. Institut für Informatik, Technische Universität, Arcisstr. 21, D-8000, München 2

    Walter Vogler

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  1. Walter Vogler
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Hartmut Ehrig Hans-Jörg Kreowski Grzegorz Rozenberg

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© 1991 Springer-Verlag Berlin Heidelberg

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Vogler, W. (1991). Recognizing edge replacement graph languages in cubic time. In: Ehrig, H., Kreowski, HJ., Rozenberg, G. (eds) Graph Grammars and Their Application to Computer Science. Graph Grammars 1990. Lecture Notes in Computer Science, vol 532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017421

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  • DOI: https://doi.org/10.1007/BFb0017421

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54478-4

  • Online ISBN: 978-3-540-38395-6

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