Context-Sensitive Fusion Grammars Are Universal

Context-sensitive fusion grammars are a special case of context-dependent fusion grammars where a rule has only a single positive context condition instead of finite sets of positive and negative context conditions. They generate hypergraph languages from start hypergraphs via successive applications of context-sensitive fusion rules and multiplications of connected components, as well as a filtering mechanism to extract terminal hypergraphs from derived hypergraphs in a certain way. The application of a context-sensitive fusion rule consumes two complementarily labeled hyperedges and identifies corresponding attachment vertices provided that the context condition holds. In this paper, we show that the Post correspondence problem can be formulated very intuitively by such a grammar. Furthermore, we prove that these grammars can generate all recursively enumerable string languages (up to representation of strings as graphs) and are universal in this respect.