Criteria to Disprove Context-Freeness of Collage Languages

. Collage grammars generate picture languages in a context-free way. The generating process is based on the replacement of atomic nonterminal items and can be seen as an adaptation of the notion of hyperedge replacement known from the area of context-free graph generation. While a pumping lemma holds for hyperedge replacement graph grammars and is quite useful to show that certain graph languages cannot be generated, the same technique fails in the collage case, unfortunately. But, in this paper, we present some other criteria that allow to disprove context freeness of collage languages. 1 Introduction Collage grammars are context-free devices for the generation of d-dimensional picture languages (see, e.g., [HKT93,DHKT95,DK96,Dre96]). A collage consists of a set of parts (each part being a set of points in a euclidean space of some dimension) where the overlay of the parts yields the picture. The generation of collages is based on the replacement of nonterminals and is closely relate..