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International Symposium on Mathematical Foundations of Computer Science

MFCS 1998: Mathematical Foundations of Computer Science 1998 pp 616–624Cite as

Facial circuits of planar graphs and context-free languages

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

It is known that a language is context-free iff it is the set of borders of the trees of recognizable set, where the border of a (labelled) tree is the word consisting of its leaf labels read from left to right.

We give a generalization of this result in terms of planar graphs of bounded tree-width. Here the border of a planar graph is the word of edge labels of a path which borders a face for some planar embedding. We prove that a language is context-free iff it is the set of borders of the graphs of a set of (labelled) planar graphs of bounded tree-width which is definable by a formula of monadic second-order logic.

Research partly supported by the EC TMR Network GETGRATS (General Theory of Graph Transformation Systems).

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Author information

Authors and Affiliations

  1. LaBRI (UMR 5800, CNRS), Université Bordeaux, 351, cours de la Libération, 33405, Talence Cedex, France

    Bruno Courcelle

  2. University of Bremen, P.O. Box 33 04 40, D-28334, Bremen, Germany

    Denis Lapoire

Authors
  1. Bruno Courcelle
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  2. Denis Lapoire
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Editor information

Luboš Brim Jozef Gruska Jiří Zlatuška

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© 1998 Springer-Verlag Berlin Heidelberg

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Courcelle, B., Lapoire, D. (1998). Facial circuits of planar graphs and context-free languages. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055812

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  • DOI: https://doi.org/10.1007/BFb0055812

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

  • eBook Packages: Springer Book Archive

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