The Equivalence of Tree Adjoining Grammars and Monadic Linear Context-free Tree Grammars

Abstract
The equivalence of leaf languages of tree adjoining grammars and monadic linear context-free grammars was shown about a decade ago. This paper presents a proof of the strong equivalence of these grammar formalisms. Non-strict tree adjoining grammars and monadic linear context-free grammars define the same class of tree languages. We also present a logical characterisation of this tree language class showing that a tree language is a member of this class iff it is the two-dimensional yield of an MSO-definable three-dimensional tree language
Keywords Tree adjoining grammar  Monadic linear context-free tree grammar  Monadic second-order logic  Model theoretic syntax
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