Picture languages: Tiling systems versus tile rewriting grammars.

Theor. Comput. Sci 01/2006; 356:90-103. DOI: 10.1016/j.tcs.2006.01.038
Source: DBLP

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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