Monadic Second-Order Evaluations on Tree-Decomposable Graphs

Abstract Every graph generated by a hyperedge replacement graph-grammar can be represented by a tree, namely the derivation tree of the derivation sequence that produced it. Certain functions on graphs can be computed recursively on the derivation trees of these graphs. By using monadic second-order logic and semiring homomorphisms, we describe in a single formalism a large class of such functions. Polynomial and even linear algorithms can be constructed for some of these functions. We unify similar results obtained by Takamizawa (1982), Bern (1987), Arnborg (1991) and Habel (1989).

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