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Indexed Grammars—An Extension of Context-Free Grammars

Alfred V. Aho

Abstract

A new type of grammar for generating formal languages, called an indexed grammar, is presented. An indexed grammar is an extension of a context-free grammar, and the class of languages generated by indexed grammars has closure properties and decidability results similar to those for context-free languages. The class of languages generated by indexed grammars properly includes all context-free languages and is a proper subset of the class of context-sensitive languages. Several subclasses of indexed grammars generate interesting classes of languages.

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Key concepts: Tree-adjoining grammar, Indexed grammar, L-attributed grammar, Context-sensitive grammar, Context-free grammar, Computer science, Programming language, Phrase structure grammar