Picture languages: tiling systems versus tile rewriting grammars

Authors:
Alessandra Cherubini;Stefano Crespi Reghizzi;Matteo Pradella;Pierluigi San Pietro
Affiliations:
Politecnico di Milano, Milano, Italy;Politecnico di Milano, Milano, Italy and CNR IEIIT-MI, Milano, Italy;CNR IEIIT-MI, Milano, Italy;Politecnico di Milano, Milano, Italy
Venue:
Theoretical Computer Science - In honour of Professor Christian Choffrut on the occasion of his 60th birthday
Year:
2006

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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.