Picture languages: Tiling systems versus tile rewriting grammars

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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.

Keywords

Picture language
Picture grammar
2D language
Tiling system
Recognizable picture language
Tile rewriting grammar
2D regular expression
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Work partially supported by MIUR, Progetto Linguaggi formalie automi, teoria e applicazioni.