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MFCS
1998
Springer

Facial Circuits of Planar Graphs and Context-Free Languages

9 years 14 days ago
Facial Circuits of Planar Graphs and Context-Free Languages
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. Thatcher and Wright [12] (see also Doner [5]) characterize context-free languages as the images of the recognizable sets of finite trees under a mapping border that produces for each given tree the sequence of symbols labeling its leaves, read from left to right. Our aim is to extend such a characterization to Monadic Second Order definable sets of graphs. Here, the borde...
Bruno Courcelle, Denis Lapoire
Added 06 Aug 2010
Updated 06 Aug 2010
Type Conference
Year 1998
Where MFCS
Authors Bruno Courcelle, Denis Lapoire
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