A note on array grammars (Q793512)

In this note some results concerning isometric array grammars are given. It is shown that the following families of languages are equal: i) the family of pattern languages generated by two-dimensional (2-D) context sensitive grammars and the family of languages generated by isometric array grammars; ii) the family of pattern languages generated by monotonic array grammars; iii) the family of pattern languages generated by 2-D context-free grammars and the family of context free array languages; iv) the family of pattern languages generated by 2-D linear grammars and the family of linear array languages.