Abstract
Every set of finite graphs definable in monadic second-order logic is recognizable in the algebraic sense of Mezei and Wright (no "graph automaton" is provided). We apply this result to the comparison of several definitions of sets of finite graphs , in particular by context-free graph grammars, and by forbidden configurations. It follows that the monadic second order theory of a context-free set of graphs is decidable, and that every graph property expressible in monadic second-order logic is decidable in polynomial time for graphs of a given maximal tree-width.
Notes: (+) Unité de Recherche Associée au CNRS no726 This work has been supported by the "Programme de Recherches Coordonnées : Mathématiques et Informatique " Electronic mail : mcvax!inria!geocub!courcell (on UUCP network) or : courcell (at) inria.geocub.
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Courcelle, B. (1989). The monadic second-order logic of graphs : Definable sets of finite graphs. In: van Leeuwen, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 1988. Lecture Notes in Computer Science, vol 344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50728-0_34
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DOI: https://doi.org/10.1007/3-540-50728-0_34
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