The global index languages are a subset of the context sensitive languages, and a superset of the context free languages.
2.
However, the context sensitive languages and the recursive languages are AFLs, but not full AFLs because they are not closed under arbitrary homomorphisms.
3.
More recently, the class PTIME has been identified with range concatenation grammars, which are now considered to be the most expressive of the mild-context sensitive languages.
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