Indexed Grammars—An Extension of Context-Free Grammars

  • Authors:
  • Alfred V. Aho

  • Affiliations:
  • Bell Telephone Laboratories, Inc., Murray Hill, New Jersey

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1968

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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.