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On polynomial time graph grammars

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STACS 88 (STACS 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 294))

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Abstract

The complexity of node rewriting graph grammars is investigated, i.e. the membership problem for sets of graphs L(G) generated by directed, node and edge label controlled graph grammars G. We improve known results on the membership problem and comprise them into the following sharp characterization of the P vs. NP borderline, which is an "if and only if" result.

∀G: (fCR ∧ connected ∧ bounded degree) then L(G) is in P.

∃G: not (fCR ∧ connected ∧ bounded degree) and L(G) is NP hard.

Here, fCR means that the graph grammar G has the finite Church Rosser property, and connected and bounded degree means that the graphs in the generated language L(G) are connected and of bounded degree.

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Authors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Passau, D 8390, Passau, Federal Republic of Germany

    Franz J. Brandenburg

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  1. Franz J. Brandenburg
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Robert Cori Martin Wirsing

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© 1988 Springer-Verlag Berlin Heidelberg

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Brandenburg, F.J. (1988). On polynomial time graph grammars. In: Cori, R., Wirsing, M. (eds) STACS 88. STACS 1988. Lecture Notes in Computer Science, vol 294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035847

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  • DOI: https://doi.org/10.1007/BFb0035847

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18834-6

  • Online ISBN: 978-3-540-48190-4

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