Regional Languages and Tiling: A Unifying Approach to Picture Grammars

Several classical models of picture grammars based on array rewriting rules can be unified and extended by a tiling based approach. The right part of a rewriting rule is formalized by a finite set of permitted tiles. We focus on a simple type of tiling, named regional, and define the corresponding regional tile grammars. They include both Siromoney’s (or Matz’s) Kolam grammars, and their generalization by Prusa. Regionally defined pictures can be recognized with polynomial time complexity by an algorithm extending the CKY one for strings. Regional tile grammars and languages are strictly included into the tile grammars and languages, and are incomparable with Giammarresi-Restivo tiling systems (or Wang’s tilings).