A property of random context picture grammars

Authors:
Andries van der Walt;Sigrid Ewert
Affiliations:
Department of Computer Science, University of Stellenbosch, Stellenbosch, South Africa;School of Computer Science, University of the Witwatersrand, Private Bag 3, Wits, 2050 Johannesburg, South Africa
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

We use random context picture grammers to generate pictures through successive refinement. The productions of such a grammar are context free, but their application is regulated by context randomly distributed in the developing picture. Grammars using this relatively weak context often succeed where context-free grammars fail, e.g., in generating the typical iteration sequence of the Sierpiński carpet. On the other hand, it proved possible to develop iteration theorems for three subclasses of these grammars; finding necessary conditions is problematic in the case of most models of context-free picture grammars with context-sensing ability, since they consider a variable and its context as a connected unit.We present a property of all picture sets generated with random context picture grammers, and then construct a picture set that does not belong to this class.