Picture languages: Tiling systems versus tile rewriting grammars

Theoretical Computer Science (Impact Factor: 0.52). 05/2006; 356(1-2):90-103. DOI: 10.1016/j.tcs.2006.01.038
Source: DBLP

ABSTRACT 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.

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