Two formal models of pictures, i.e., two dimensional (2D) languages are compared: tiling systems and tile rewriting grammars, which resp. extend to 2D the regular and context-free languages. Two results extending classical language properties into 2D are proved. First, non-recursive tile writing grammars (TRG) coincide with tiling systems (TS). Second, non-self-embedding TRG are suitably defined as corner grammars, showing that they generate TS languages. The proofs exploit newly introduced language substitutions, also nested and iterated.
['Alessandra Cherubini', 'Stefano Crespi Reghizzi', 'Matteo Pradella', 'Pierluigi San Pietro']
Picture languages: tiling systems versus tile rewriting grammars