Tile Rewriting Grammars
Past proposals for applying to pictures or 2D languages the generative grammar approach do not match in our opinion the elegance and descriptive adequacy that made Context Free grammars so successful for 1D languages. In a renewed attempt, a model named Tile Rewriting Grammar is introduced combining the rewriting rules with the Tiling System of Giammaresi and Restivo which define the family of Recognizable 2D languages. The new grammars have isometric rewriting rules which for string languages are equivalent to CF rules. TRG have the capacity to generate a sort of 2D analogues of Dyck languages. Closure properties of TRG are proved for some basic operations. TRG strictly include TS as well as the context-free picture grammars of Matz.
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