Criteria to disprove context freeness of collage languages

Authors:
Frank Drewes;Hans-Jörg Kreowski;Denis Lapoire
Affiliations:
Department of Computing Science, Umeå University, S-901 87 Umeå, Sweden;Department of Computer Science, University of Bremen, P.O. Box 33 04 40, D-28334 Bremen, Germany;LaBRI, Université Bordeaux I, 351, cours de la liberation, 33400 Talence Cedex, France
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

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 difficulty, 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 can be deflated stepwise in such a manner that the difference between subsequent collages in the resulting chain is small and (2) the volume of parts can grow or shrink only exponentially.