Criteria to disprove context freeness of collage languages

Frank Drewes, Hans-Jörg Kreowski, Denis Lapoire
2003 Theoretical Computer Science  
Collage grammars are context-free devices which generate picture languages consisting of collages-sets of parts, where a part is a set of points in a given space. In order to show that certain collage languages cannot be generated, the well-known pumping technique turns out to be rather useless. To circumvent this di culty, other necessary criteria for context-freeness are established in this paper. Roughly speaking, these criteria reveal that (1) the collages in a context-free collage language
more » ... can be de ated stepwise in such a manner that the di erence between subsequent collages in the resulting chain is small and (2) the volume of parts can grow or shrink only exponentially.
doi:10.1016/s0304-3975(02)00049-x fatcat:45azuwgodza7hiqwt62xron2ym