Picture languages: Tiling systems versus tile rewriting grammars.
ABSTRACT Two formal models of pictures, i.e., 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 TRG coincide with 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.
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ABSTRACT: Several old and recent classes of picture grammars, that variously extend context-free string grammars in two dimensions, are based on rules that rewrite arrays of pixels. Such grammars can be unified and extended using a tiling based approach, whereby the right part of a rule is formalized by means of 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, as well as Drewes's grid grammars. 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 our previous tile grammars and languages, and are incomparable with Giammarresi-Restivo tiling systems (or Wang systems).Computing Research Repository - CORR. 10/2009;
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ABSTRACT: A concept of a generalized Gandy-Păun-Rozenberg machine for modelling various systems of multidimensional tile-like compartments with common parts (tile faces) of compartment boundaries by graph rewriting is introduced, where some massive parallelism of computations or evolution processes generated by these systems is respected. The representation of Gandy---Păun---Rozenberg machines by Gandy machines in  is extended to the case of generalized Gandy---Păn---Rozenberg machines, where the machines represented by Gandy machines are equivalent to Turing machines.Membrane Computing - 12th International Conference, CMC 2011, Fontainebleau, France, August 23-26, 2011, Revised Selected Papers; 01/2011
- Fundam. Inform. 01/2011; 110:77-93.