On polynomial time graph grammars
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The complexity of node rewriting graph grammars is investigated, i.e. the membership problem for sets of graphs L(G) generated by directed, node and edge label controlled graph grammars G. We improve known results on the membership problem and comprise them into the following sharp characterization of the P vs. NP borderline, which is an "if and only if" result.
∀G: (fCR ∧ connected ∧ bounded degree) then L(G) is in P.
∃G: not (fCR ∧ connected ∧ bounded degree) and L(G) is NP hard.
Here, fCR means that the graph grammar G has the finite Church Rosser property, and connected and bounded degree means that the graphs in the generated language L(G) are connected and of bounded degree.
KeywordsPolynomial Time Edge Label Node Label Derivation Tree Graph Grammar
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