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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© 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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