Indexed grammars -- An extension of context free grammars

Abstract

A new type of grammar, called an indexed grammar, is defined. The language generated by an indexed grammar is called an indexed language. The class of indexed languages properly includes the class of context free languages and is a proper subset of the class of context sensitive languages. The closure properties and decidability results for the class of indexed languages are similar to those for the class of context free languages. An exact characterization of this new class of languages is provided by a new recognition device called a nested stack automaton. Special cases of the nested stack automaton include the pushdown automaton, the stack automaton, and the reading pushdown automaton. The class of indexed languages seems to be a closer approximation to the class of algorithmic programming languages than either the class of context free languages or the class of context sensitive languages.