Abstract
We present conditions under which graph transformation rules can be applied in time independent of the size of the input graph: graphs must contain a unique root label, nodes in the left-hand sides of rules must be reachable from the root, and nodes must have a bounded outdegree. We establish a constant upper bound for the time needed to construct all graphs resulting from an application of a fixed rule to an input graph. We also give an improved upper bound under the stronger condition that all edges outgoing from a node must have distinct labels. Then this result is applied to identify a class of graph reduction systems that define graph languages with a linear membership test. In a case study we prove that the (non-context-free) language of balanced binary trees with backpointers belongs to this class.
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Dodds, M., Plump, D. (2006). Graph Transformation in Constant Time. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds) Graph Transformations. ICGT 2006. Lecture Notes in Computer Science, vol 4178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841883_26
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DOI: https://doi.org/10.1007/11841883_26
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