Two-dimensional Picture Grammar models

Abstract

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.

Adjunct hexagonal array token Petri nets and hexagonal picture languages

“…We denote by (R)HCF L pure the family of hexagonal picture languages generated by pure 2D hexagonal context-free grammars with regular control. To increase the generating power of (R)HCF G pure further, we refine the definition of this class of grammars like that of pure 2D rectangular picture grammars considered in [14] but adapted as in [2]. Definition 4.4.…”

“…In a chromosome analysis program [9], the circumscribing polygons associated with each image turn out to be hexagons. Since late seventies, formal models to generate or recognize the hexagonal pictures have been found in the literature [3,[5][6][7]12,14] in the framework of pattern recognition and image analysis. Some of the classical formalisms to generate hexagonal arrays are Hexagonal Kolam Array Grammars (HKAG) [12] and its generalization Hexagonal Array Grammars (HAG) [13].…”

“…Hexagonal Tile Rewriting Grammars [16] and Regional Hexagonal Tile Rewriting Grammars [5] are the recent hexagonal tiling based isometric grammar models, which have more generative capacity than HAG. Differently, Pure 2D Hexagonal Context Free Grammars [14,15] and Hexagonal Prusa Grammars [6] are the simple yet expressive non-isometric formalisms, where parallel application of rewriting rules are attempted in the derivation of hexagonal pictures. On the MSC (2010): primary 68Q42, 68Q45.…”

Picture Array Generation Based on Membrane Systems and 2D Context-Free Grammars

“…We now recall extended 2D context-free picture grammar considered in [11]. In an E2DCFPG, unlike 2D matrix grammar, there is single phase of derivation.…”

“…In generating a picture array language L, this 2D grammar involves only terminal symbols and rewrites at a derivation step, all the symbols in a column or row of a picture array making use of a finite set of context-free string grammar rules, thereby yielding the picture arrays of L. There has been other investigation [1] on the mathematical properties of the picture language family of P2DCFG. An extension to this 2D grammar model, called extended 2D context-free picture grammar (E2DCFPG), with more picture generative power than the P2DCFPG was proposed in [11] by allowing variables in the rules of this picture grammar model and collecting the picture arrays generated over a set of terminal symbols.…”