Abstract

Traditional spatial enabled grammars lack flexibility in specifying the spatial semantics of graphs. This paper describes a new graph grammar formalism called the multigranularity Coordinate Graph Grammar (mgCGG) for spatial graphs. Based on the Coordinate Graph Grammar (CGG), the mgCGG divides coordinates into two categories, physical coordinates and grammatical coordinates, where physical coordinates are the common coordinates in the real world, and grammatical coordinates describe the restrictions on the spatial semantics. In the derivation and reduction of the mgCGG, the spatial matching conditions between nodes are evaluated on the basis of the grammatical coordinates, which can be obtained by the specified granularities. By adjusting the granularities, both qualitative and quantitative analyses for spatial semantics can be obtained, including the transition states between them. In addition, a new redex searching algorithm with polynomial time complexity is designed for the mgCGG. A running example of drawing a flowchart is given to illustrate a practical application of the mgCGG. Through a detailed comparison with related spatial-enabled grammars, it is found that the mgCGG has good performance in four critical aspects—the semantics processing mechanism, fault-tolerance, redex searching algorithm, and practical application—providing a flexible yet uniform way to specify spatial graphs and building a bridge between nonspatial and spatial grammars.