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...

• Type: Conference
• Year: 1998
• Where: MFCS
• Authors: Bruno Courcelle, Denis Lapoire
• Keywords: Context-free, MFCS 1998, Planar Graphs, Recognizable Sets, Theoretical Computer Science