Tree-oriented proofs of some theorems on context-free and indexed languages

Abstract

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 [l ]. Standard results on context-free languages can be obtained quickly using this theorem. We consider here the Peters-Ritchie theorem [U ] : 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.