Abstract
This paper deals with a class of grammars which is called tree-graph grammar (TGG) and its attributed version (ATGG, attributed-tree-graph grammar). The features of this class of grammars include its power to generate useful graphs and its fast parser. Principally, the graphs that can be characterized by these grammars are a subset of hierarchical graphs, including planar graphs. Also these TGG's (and ATGG's) can generate graphs describing, for example, textures, flow charts, circuit diagrams, etc. It is proved that the class of context-free graph grammars (CFGG) is a subclass of TGG's. Also it is shown that TGG can generate graphs which can not be produced by CFGG's, for example, planar graphs. Moreover, a parser for ATGG's is proposed. This parser has time complexity of 0(n4) (n is the number of nodes of the graph plus the number of superimposed nodes), and space complexity of 0(n2). For the special case where the starting node is given, the time complexity is reduced to 0(n3). Finally, an application of ATGG's to the recognition of circuit diagrams is presented.
This work is supported in part by the NSF Grant ECS 78-16970. The research was performed when A. Sanfeliu was visiting Purdue University in 1979–81.
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© 1983 Springer-Verlag Berlin Heidelberg
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Sanfeliu, A., Fu, K.S. (1983). Tree-graph grammars for pattern recognition. In: Ehrig, H., Nagl, M., Rozenberg, G. (eds) Graph-Grammars and Their Application to Computer Science. Graph Grammars 1982. Lecture Notes in Computer Science, vol 153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000118
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DOI: https://doi.org/10.1007/BFb0000118
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