Indexed languages are a class of formal languages discovered by Alfred Aho;[1] they are described by indexed grammars and can be recognized by nested stack automata.[2]
Indexed languages are a proper subset of context-sensitive languages.[1] They qualify as an abstract family of languages (furthermore a full AFL) and hence satisfy many closure properties. However, they are not closed under intersection or complement.[1]
The class of indexed languages has practical importance in natural language processing as a computationally affordable[citation needed] generalization of context-free languages, since indexed grammars can describe many of the nonlocal constraints occurring in natural languages.
Gerald Gazdar (1988)[3] and Vijay-Shanker (1987)[4] introduced a mildly context-sensitive language class now known as linear indexed grammars (LIG).[5] Linear indexed grammars have additional restrictions relative to IG. LIGs are weakly equivalent (generate the same language class) as tree adjoining grammars.[6]
^ abcAho, Alfred (1968). "Indexed grammars—an extension of context-free grammars". Journal of the ACM. 15 (4): 647–671. doi:10.1145/321479.321488. S2CID 9539666.
^Partee, Barbara; ter Meulen, Alice; Wall, Robert E. (1990). Mathematical Methods in Linguistics. Kluwer Academic Publishers. pp. 536–542. ISBN 978-90-277-2245-4.
^Gazdar, Gerald (1988). "Applicability of Indexed Grammars to Natural Languages". In Reyle, U.; Rohrer, C. (eds.). Natural Language Parsing and Linguistic Theories. Studies in Linguistics and Philosophy. Vol. 35. Springer Netherlands. pp. 69–94. doi:10.1007/978-94-009-1337-0_3. ISBN 978-94-009-1337-0.
^Vijayashanker, K. (1987). A study of tree adjoining grammars (Thesis). ProQuest 303610666.
^Kallmeyer, Laura (2010). Parsing Beyond Context-Free Grammars. Springer. p. 31. ISBN 978-3-642-14846-0.
^Kallmeyer, Laura (16 August 2010). Parsing Beyond Context-Free Grammars. Springer. p. 32. ISBN 978-3-642-14846-0.
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is capable of recognizing an indexedlanguage, and in fact the class of indexedlanguages is exactly the class of languages accepted by one-way nondeterministic...
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