On the structure of context-sensitive grammars

It is well known that the family of context-sensitive grammars generate languages which are not context-free and that it is undecidable whether a context-sensitive grammar generates a context-free language. However, the mechanism by which the use of context allows a non-context-free language to be generated is not well understood. In this paper we attempt to focus on this problem by surveying some of the results which speak to two questions: (i) What constraints can be placed on the form of the rules of context-sensitive grammars without restricting the weak generative capacity? (ii) What (nontrivial) constraints can be placed on the form of the rules of context-sensitive grammars such that only context-free languages will be generated?

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