In this note a new model of grammatical picture generation is introduced. The model is based on the notion of pure context-free grammars of formal string language theory. The resulting model, called Pure 2D context-free grammar (CFG), generates rectangular picture arrays of symbols. The generative power of this model in comparison to certain other related models is examined. Also we associate a regular control language with a Pure 2D CFG and notice that the generative power increases. Certain closure properties are obtained.
A new theoretical model of grammatical picture generation called extended 2D context-free picture grammar (E2DCFPG) generating rectangular picture arrays of symbols is introduced. This model which allows variables in the grammar and uses the squeezing mechanism of forming the picture language over terminal symbols, is an extension of the pure 2D context-free picture grammar (P2DCFPG) [13]. The extended picture grammar model E2DCFPG is shown to have more picture generative power than the P2DCFPG and certain other existing 2D models. Certain closure and other properties of this new model are also examined.
A new syntactic model, called pure two-dimensional (2D) context-free grammar (P2DCFG), is introduced based on the notion of pure context-free string grammar. The rectangular picture generative power of this 2D grammar model is investigated. Certain closure properties are obtained. An analogue of this 2D grammar model called pure 2D hexagonal context-free grammar (P2DHCFG) is also considered to generate hexagonal picture arrays on triangular grids
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