Indexed languages are a proper subset of context-sensitive languages.
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The class of indexed languages has generalization of context-free languages, since indexed grammars can describe many of the nonlocal constraints occurring in natural languages.
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The linearly indexed languages are a subset of the indexed languages, and thus all LIGs can be recoded as IGs, making the LIGs strictly less powerful than the IGs.
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The linearly indexed languages are a subset of the indexed languages, and thus all LIGs can be recoded as IGs, making the LIGs strictly less powerful than the IGs.
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A nested stack automaton is capable of recognizing an indexed language, and in fact the class of indexed languages is exactly the class of languages accepted by one-way nondeterministic nested stack automata.
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A nested stack automaton is capable of recognizing an indexed language, and in fact the class of indexed languages is exactly the class of languages accepted by one-way nondeterministic nested stack automata.
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CCGs are known to be able to generate the language { a ^ n b ^ n c ^ n d ^ n : n \ geq 0 } ( which is an indexed language ).
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While it is known that GIGs can generate the MIX / Bach language \ { p ( a ^ n b ^ n c ^ n ) : n \ geq 1 \ }, where " p " is the string permutation function, and thus are capable of generating non-indexed languages, it is not known whether or not all IGs are also GIGs.
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