Indexed Grammars—An Extension of Context-Free Grammars
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In this paper we study some applications and generalizations of the yield theorem: the yield of a recognizable set of trees (dendrolanguage) is an indexed language [1]. Standard results on context-free languages can be obtained quickly using this theorem. We consider here the Peters-Ritchie theorem [4]: the language analyzable by a finite set of CS rules is CF. An extension of the yield theorem reads: the yield of a CF set of trees is an indexed language. We prove some closure properties of CF sets of trees. Applying the yield theorem, we obtain properties of indexed languages. As a special result, we can solve the infiniteness problem for such languages.