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. © Springer-Verlag Berlin Heidelberg 2009.
Bonizzoni, P., Ferretti, C., Anthonath Roslin Sagaya, M., Mauri, G. (2009). Picture languages generated by assembling tiles. In Language and Automata Theory and Applications (pp.224-235). Berlin : Springer-Verlag [10.1007/978-3-642-00982-2_19].
Picture languages generated by assembling tiles
BONIZZONI, PAOLA;FERRETTI, CLAUDIO;MAURI, GIANCARLO
2009
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. © Springer-Verlag Berlin Heidelberg 2009.
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