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.
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Kepser, S., Rogers, J. The Equivalence of Tree Adjoining Grammars and Monadic Linear Context-free Tree Grammars. J of Log Lang and Inf 20, 361–384 (2011). https://doi.org/10.1007/s10849-011-9134-0
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DOI: https://doi.org/10.1007/s10849-011-9134-0