Picture Languages Generated by Assembling Tiles

Authors:
Paola Bonizzoni;Claudio Ferretti;Anthonath Roslin Sagaya Mary;Giancarlo Mauri
Affiliations:
Dipartimento di Informatica Sistemistica e Comunicazione, Università degli Studi di Milano --- Bicocca, Milano, Italy 20126;Dipartimento di Informatica Sistemistica e Comunicazione, Università degli Studi di Milano --- Bicocca, Milano, Italy 20126;Dipartimento di Informatica Sistemistica e Comunicazione, Università degli Studi di Milano --- Bicocca, Milano, Italy 20126;Dipartimento di Informatica Sistemistica e Comunicazione, Università degli Studi di Milano --- Bicocca, Milano, Italy 20126
Venue:
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Year:
2009

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Abstract

We propose a new formalism for generating picture languages based on an assembly mechanism of tiles that uses rules having a context and a replacement site. More precisely, a picture language will be generated from a finite set of initial pictures by iteratively applying rewriting rules from a given finite set of rules, called a tiling rule system (TRuS system). We prove that the TRuS systems have a greater generative capacity than the tiling systems of Giammarresi and Restivo, even in the case of one-letter alphabet picture languages. This is due mainly to the use of the notion of replacement.