Facial circuits of planar graphs and context-free languages

  • Bruno Courcelle
  • Denis Lapoire
Contributed Papers Binary Decision Diagrams
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1450)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Bruno Courcelle
    • 1
  • Denis Lapoire
    • 2
  1. 1.LaBRI (UMR 5800, CNRS)Université BordeauxTalence CedexFrance
  2. 2.University of BremenBremenGermany

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