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We prove that for each k, there exists a MSO-transduction that associates with every graph of tree-width at most k one of its tree-decompositions of width at most k. Courcelle proves in (The Monadic second-order logic of graphs, I: Recognizable sets of nite graphs) that every set of graphs is recognizable if it is deenable in Counting Monadic Second-Order… (More)

Collage grammars generate picture languages in a context-free way. The generating process is based on the replacement of atomic nonterminal items and can be seen as an adaptation of the notion of hyperedge replacement known from the area of context-free graph generation. While a pumping lemma holds for hyperedge replacement graph grammars and is quite… (More)

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… (More)

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